LMFDB - Embedded newform 399.2.ck.a.10.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [399,2,Mod(10,399)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("399.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(399, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 3, 17])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 399 = 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	399.ck (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [78] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.18603104065$
Analytic rank:	$0$
Dimension:	$78$
Relative dimension:	$13$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			10.6
Character	$\chi$	$=$	399.10
Dual form			399.2.ck.a.40.6

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.376037 - 0.448144i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.287868 - 1.63258i) q^{4} +(-2.56641 + 0.452528i) q^{5} +(-0.376037 + 0.448144i) q^{6} +(0.436486 + 2.60950i) q^{7} +(-1.85315 + 1.06991i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(1.16786 + 0.979954i) q^{10} -5.54502 q^{11} -1.65776 q^{12} +(2.54738 + 2.13751i) q^{13} +(1.00529 - 1.17688i) q^{14} +(0.891305 + 2.44884i) q^{15} +(-1.93925 - 0.705829i) q^{16} +(0.984567 - 2.70508i) q^{17} +(0.506633 + 0.292505i) q^{18} +(-3.68173 + 2.33342i) q^{19} +4.32014i q^{20} +(2.49406 - 0.882990i) q^{21} +(2.08513 + 2.48497i) q^{22} +(2.63403 + 2.21021i) q^{23} +(1.37545 + 1.63920i) q^{24} +(1.68322 - 0.612643i) q^{25} -1.94537i q^{26} +(0.500000 + 0.866025i) q^{27} +(4.38586 + 0.0385916i) q^{28} +(-1.71323 - 0.302088i) q^{29} +(0.762269 - 1.32029i) q^{30} +(0.478361 + 0.828545i) q^{31} +(1.87665 + 5.15604i) q^{32} +(0.962883 + 5.46078i) q^{33} +(-1.58250 + 0.575982i) q^{34} +(-2.30107 - 6.49952i) q^{35} +(0.287868 + 1.63258i) q^{36} +(-2.53159 + 1.46161i) q^{37} +(2.43018 + 0.772490i) q^{38} +(1.66269 - 2.87986i) q^{39} +(4.27177 - 3.58444i) q^{40} +(2.20303 - 1.84856i) q^{41} +(-1.33356 - 0.785660i) q^{42} +(-9.72015 - 3.53785i) q^{43} +(-1.59623 + 9.05268i) q^{44} +(2.25686 - 1.30300i) q^{45} -2.01155i q^{46} +(-0.301717 - 0.828962i) q^{47} +(-0.358359 + 2.03235i) q^{48} +(-6.61896 + 2.27802i) q^{49} +(-0.907506 - 0.523949i) q^{50} +(-2.83495 - 0.499878i) q^{51} +(4.22296 - 3.54348i) q^{52} +(-11.9733 - 2.11122i) q^{53} +(0.200085 - 0.549730i) q^{54} +(14.2308 - 2.50928i) q^{55} +(-3.60081 - 4.36878i) q^{56} +(2.93730 + 3.22060i) q^{57} +(0.508858 + 0.881367i) q^{58} +(-3.59116 - 1.30708i) q^{59} +(4.25450 - 0.750184i) q^{60} +(7.26059 - 8.65283i) q^{61} +(0.191426 - 0.525938i) q^{62} +(-1.30266 - 2.30284i) q^{63} +(-0.458748 + 0.794574i) q^{64} +(-7.50491 - 4.33296i) q^{65} +(2.08513 - 2.48497i) q^{66} +(2.74107 - 3.26668i) q^{67} +(-4.13282 - 2.38609i) q^{68} +(1.71924 - 2.97781i) q^{69} +(-2.04743 + 3.47527i) q^{70} +(-5.37413 + 14.7653i) q^{71} +(1.37545 - 1.63920i) q^{72} +(-11.2302 + 1.98018i) q^{73} +(1.60699 + 0.584895i) q^{74} +(-0.895624 - 1.55127i) q^{75} +(2.74964 + 6.68243i) q^{76} +(-2.42033 - 14.4697i) q^{77} +(-1.91582 + 0.337811i) q^{78} +(1.63730 - 4.49843i) q^{79} +(5.29632 + 0.933884i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-1.65684 - 0.292146i) q^{82} +(10.4422 + 6.02883i) q^{83} +(-0.723591 - 4.32593i) q^{84} +(-1.30268 + 7.38788i) q^{85} +(2.06968 + 5.68639i) q^{86} +1.73966i q^{87} +(10.2757 - 5.93270i) q^{88} +(-0.293180 + 1.66271i) q^{89} +(-1.43260 - 0.521422i) q^{90} +(-4.46592 + 7.58038i) q^{91} +(4.36660 - 3.66401i) q^{92} +(0.732891 - 0.614969i) q^{93} +(-0.258037 + 0.446933i) q^{94} +(8.39290 - 7.65461i) q^{95} +(4.75183 - 2.74347i) q^{96} +(-0.923961 - 5.24005i) q^{97} +(3.50985 + 2.10962i) q^{98} +(5.21062 - 1.89651i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q - 6 q^{7} + 12 q^{10} + 6 q^{11} + 72 q^{12} + 3 q^{13} - 15 q^{14} + 18 q^{19} + 9 q^{21} - 12 q^{22} + 30 q^{23} - 9 q^{24} + 18 q^{25} + 39 q^{27} - 9 q^{28} - 6 q^{29} - 18 q^{31} - 51 q^{32} - 12 q^{33}+ \cdots - 6 q^{99}+O(q^{100}) $ 78 * q - 6 * q^7 + 12 * q^10 + 6 * q^11 + 72 * q^12 + 3 * q^13 - 15 * q^14 + 18 * q^19 + 9 * q^21 - 12 * q^22 + 30 * q^23 - 9 * q^24 + 18 * q^25 + 39 * q^27 - 9 * q^28 - 6 * q^29 - 18 * q^31 - 51 * q^32 - 12 * q^33 + 30 * q^34 + 33 * q^35 + 18 * q^37 - 57 * q^38 - 18 * q^40 - 63 * q^41 - 27 * q^42 - 51 * q^43 - 36 * q^44 + 9 * q^45 - 84 * q^47 + 18 * q^49 - 27 * q^50 - 18 * q^51 + 18 * q^52 - 45 * q^53 + 30 * q^55 + 33 * q^56 - 6 * q^57 - 18 * q^58 - 24 * q^59 + 66 * q^61 + 171 * q^62 + 6 * q^63 + 18 * q^64 - 99 * q^65 - 12 * q^66 - 24 * q^67 - 12 * q^69 - 150 * q^70 - 66 * q^71 - 9 * q^72 + 3 * q^73 + 18 * q^74 - 36 * q^75 - 12 * q^76 + 21 * q^77 + 75 * q^78 + 45 * q^79 + 78 * q^80 - 24 * q^82 - 72 * q^83 - 9 * q^84 + 60 * q^85 - 9 * q^86 - 108 * q^88 + 48 * q^89 - 33 * q^90 - 54 * q^91 - 102 * q^92 + 9 * q^93 - 66 * q^94 - 84 * q^95 + 75 * q^97 - 39 * q^98 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/399\mathbb{Z}\right)^\times$.

$n$	$115$	$134$	$211$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{17}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.376037	−	0.448144i	−0.265898	−	0.316885i	0.616531	−	0.787331i	$-0.288538\pi$
$2$	−0.376037	−	0.448144i	−0.265898	−	0.316885i	−0.882429	+	0.470446i	$0.844093\pi$
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$4$	0.287868	−	1.63258i	0.143934	−	0.816289i
$5$	−2.56641	+	0.452528i	−1.14773	+	0.202376i	−0.714986	−	0.699139i	$-0.753567\pi$
$5$	−2.56641	+	0.452528i	−1.14773	+	0.202376i	−0.432748	+	0.901515i	$0.642456\pi$
$6$	−0.376037	+	0.448144i	−0.153517	+	0.182954i
$7$	0.436486	+	2.60950i	0.164976	+	0.986298i
$7$	0.436486	+	2.60950i	0.164976	+	0.986298i
$8$	−1.85315	+	1.06991i	−0.655186	+	0.378272i
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$	1.16786	+	0.979954i	0.369311	+	0.309889i
$11$	−5.54502			−1.67189			−0.835944	−	0.548815i	$-0.815079\pi$
$11$	−5.54502			−1.67189			−0.835944	+	0.548815i	$0.815079\pi$
$12$	−1.65776			−0.478555
$13$	2.54738	+	2.13751i	0.706516	+	0.592838i	0.923619	−	0.383311i	$-0.125216\pi$
$13$	2.54738	+	2.13751i	0.706516	+	0.592838i	−0.217103	+	0.976149i	$0.569661\pi$
$14$	1.00529	−	1.17688i	0.268676	−	0.314534i
$15$	0.891305	+	2.44884i	0.230134	+	0.632288i
$16$	−1.93925	−	0.705829i	−0.484812	−	0.176457i
$17$	0.984567	−	2.70508i	0.238793	−	0.656077i	−0.761179	−	0.648542i	$-0.775379\pi$
$17$	0.984567	−	2.70508i	0.238793	−	0.656077i	0.999972	−	0.00753549i	$-0.00239864\pi$
$18$	0.506633	+	0.292505i	0.119415	+	0.0689441i
$19$	−3.68173	+	2.33342i	−0.844647	+	0.535324i
$19$	−3.68173	+	2.33342i	−0.844647	+	0.535324i
$20$			4.32014i			0.966012i
$21$	2.49406	−	0.882990i	0.544248	−	0.192684i
$22$	2.08513	+	2.48497i	0.444552	+	0.529797i
$23$	2.63403	+	2.21021i	0.549233	+	0.460861i	0.874681	−	0.484699i	$-0.161071\pi$
$23$	2.63403	+	2.21021i	0.549233	+	0.460861i	−0.325448	+	0.945560i	$0.605515\pi$
$24$	1.37545	+	1.63920i	0.280764	+	0.334601i
$25$	1.68322	−	0.612643i	0.336645	−	0.122529i
$26$		−	1.94537i		−	0.381519i
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$	4.38586	+	0.0385916i	0.828850	+	0.00729313i
$29$	−1.71323	−	0.302088i	−0.318138	−	0.0560963i	0.0122990	−	0.999924i	$-0.496085\pi$
$29$	−1.71323	−	0.302088i	−0.318138	−	0.0560963i	−0.330437	+	0.943828i	$0.607196\pi$
$30$	0.762269	−	1.32029i	0.139171	−	0.241051i
$31$	0.478361	+	0.828545i	0.0859161	+	0.148811i	0.905781	−	0.423746i	$-0.139285\pi$
$31$	0.478361	+	0.828545i	0.0859161	+	0.148811i	−0.819865	+	0.572557i	$0.805952\pi$
$32$	1.87665	+	5.15604i	0.331747	+	0.911468i
$33$	0.962883	+	5.46078i	0.167616	+	0.950600i
$34$	−1.58250	+	0.575982i	−0.271396	+	0.0987800i
$35$	−2.30107	−	6.49952i	−0.388952	−	1.09862i
$36$	0.287868	+	1.63258i	0.0479779	+	0.272096i
$37$	−2.53159	+	1.46161i	−0.416191	+	0.240288i	−0.693446	−	0.720508i	$-0.743909\pi$
$37$	−2.53159	+	1.46161i	−0.416191	+	0.240288i	0.277255	+	0.960796i	$0.410575\pi$
$38$	2.43018	+	0.772490i	0.394227	+	0.125314i
$39$	1.66269	−	2.87986i	0.266243	−	0.461146i
$40$	4.27177	−	3.58444i	0.675426	−	0.566750i
$41$	2.20303	−	1.84856i	0.344056	−	0.288697i	−0.454342	−	0.890827i	$-0.650126\pi$
$41$	2.20303	−	1.84856i	0.344056	−	0.288697i	0.798398	+	0.602130i	$0.205681\pi$
$42$	−1.33356	−	0.785660i	−0.205774	−	0.121230i
$43$	−9.72015	−	3.53785i	−1.48231	−	0.539517i	−0.530897	−	0.847436i	$-0.678145\pi$
$43$	−9.72015	−	3.53785i	−1.48231	−	0.539517i	−0.951412	+	0.307920i	$0.900367\pi$
$44$	−1.59623	+	9.05268i	−0.240641	+	1.36474i
$45$	2.25686	−	1.30300i	0.336433	−	0.194240i
$46$		−	2.01155i		−	0.296586i
$47$	−0.301717	−	0.828962i	−0.0440100	−	0.120916i	0.915741	−	0.401770i	$-0.131605\pi$
$47$	−0.301717	−	0.828962i	−0.0440100	−	0.120916i	−0.959751	+	0.280853i	$0.909383\pi$
$48$	−0.358359	+	2.03235i	−0.0517246	+	0.293345i
$49$	−6.61896	+	2.27802i	−0.945566	+	0.325432i
$50$	−0.907506	−	0.523949i	−0.128341	−	0.0740976i
$51$	−2.83495	−	0.499878i	−0.396972	−	0.0699969i
$52$	4.22296	−	3.54348i	0.585619	−	0.491392i
$53$	−11.9733	−	2.11122i	−1.64466	−	0.289998i	−0.726785	−	0.686865i	$-0.758986\pi$
$53$	−11.9733	−	2.11122i	−1.64466	−	0.289998i	−0.917876	+	0.396867i	$0.870097\pi$
$54$	0.200085	−	0.549730i	0.0272281	−	0.0748087i
$55$	14.2308	−	2.50928i	1.91888	−	0.338351i
$56$	−3.60081	−	4.36878i	−0.481179	−	0.583802i
$57$	2.93730	+	3.22060i	0.389055	+	0.426579i
$58$	0.508858	+	0.881367i	0.0668163	+	0.115729i
$59$	−3.59116	−	1.30708i	−0.467530	−	0.170167i	0.0975032	−	0.995235i	$-0.468914\pi$
$59$	−3.59116	−	1.30708i	−0.467530	−	0.170167i	−0.565033	+	0.825068i	$0.691137\pi$
$60$	4.25450	−	0.750184i	0.549254	−	0.0968483i
$61$	7.26059	−	8.65283i	0.929623	−	1.10788i	−0.0643137	−	0.997930i	$-0.520486\pi$
$61$	7.26059	−	8.65283i	0.929623	−	1.10788i	0.993937	−	0.109952i	$-0.0350697\pi$
$62$	0.191426	−	0.525938i	0.0243111	−	0.0667942i
$63$	−1.30266	−	2.30284i	−0.164120	−	0.290130i
$64$	−0.458748	+	0.794574i	−0.0573435	+	0.0993218i
$65$	−7.50491	−	4.33296i	−0.930869	−	0.537438i
$66$	2.08513	−	2.48497i	0.256662	−	0.305878i
$67$	2.74107	−	3.26668i	0.334875	−	0.399089i	−0.572161	−	0.820141i	$-0.693895\pi$
$67$	2.74107	−	3.26668i	0.334875	−	0.399089i	0.907036	+	0.421053i	$0.138339\pi$
$68$	−4.13282	−	2.38609i	−0.501178	−	0.289356i
$69$	1.71924	−	2.97781i	0.206972	−	0.358486i
$70$	−2.04743	+	3.47527i	−0.244715	+	0.415375i
$71$	−5.37413	+	14.7653i	−0.637792	+	1.75232i	0.0207593	+	0.999785i	$0.493392\pi$
$71$	−5.37413	+	14.7653i	−0.637792	+	1.75232i	−0.658552	+	0.752536i	$0.728831\pi$
$72$	1.37545	−	1.63920i	0.162099	−	0.193182i
$73$	−11.2302	+	1.98018i	−1.31439	+	0.231763i	−0.786523	−	0.617561i	$-0.788121\pi$
$73$	−11.2302	+	1.98018i	−1.31439	+	0.231763i	−0.527871	+	0.849324i	$0.677010\pi$
$74$	1.60699	+	0.584895i	0.186808	+	0.0679926i
$75$	−0.895624	−	1.55127i	−0.103418	−	0.179125i
$76$	2.74964	+	6.68243i	0.315406	+	0.766527i
$77$	−2.42033	−	14.4697i	−0.275822	−	1.64898i
$78$	−1.91582	+	0.337811i	−0.216924	+	0.0382495i
$79$	1.63730	−	4.49843i	0.184210	−	0.506113i	−0.812873	−	0.582442i	$-0.802097\pi$
$79$	1.63730	−	4.49843i	0.184210	−	0.506113i	0.997083	+	0.0763282i	$0.0243197\pi$
$80$	5.29632	+	0.933884i	0.592146	+	0.104411i
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	−1.65684	−	0.292146i	−0.182968	−	0.0322622i
$83$	10.4422	+	6.02883i	1.14619	+	0.661750i	0.947955	−	0.318405i	$-0.103147\pi$
$83$	10.4422	+	6.02883i	1.14619	+	0.661750i	0.198231	+	0.980155i	$0.436480\pi$
$84$	−0.723591	−	4.32593i	−0.0789503	−	0.471998i
$85$	−1.30268	+	7.38788i	−0.141296	+	0.801328i
$86$	2.06968	+	5.68639i	0.223179	+	0.613179i
$87$			1.73966i			0.186511i
$88$	10.2757	−	5.93270i	1.09540	−	0.632428i
$89$	−0.293180	+	1.66271i	−0.0310771	+	0.176247i	−0.996396	−	0.0848282i	$-0.972966\pi$
$89$	−0.293180	+	1.66271i	−0.0310771	+	0.176247i	0.965319	+	0.261075i	$0.0840770\pi$
$90$	−1.43260	−	0.521422i	−0.151009	−	0.0549628i
$91$	−4.46592	+	7.58038i	−0.468156	+	0.794640i
$92$	4.36660	−	3.66401i	0.455249	−	0.381999i
$93$	0.732891	−	0.614969i	0.0759973	−	0.0637693i
$94$	−0.258037	+	0.446933i	−0.0266145	+	0.0460976i
$95$	8.39290	−	7.65461i	0.861093	−	0.785346i
$96$	4.75183	−	2.74347i	0.484982	−	0.280004i
$97$	−0.923961	−	5.24005i	−0.0938141	−	0.532046i	−0.995104	−	0.0988303i	$-0.968490\pi$
$97$	−0.923961	−	5.24005i	−0.0938141	−	0.532046i	0.901290	−	0.433216i	$-0.142621\pi$
$98$	3.50985	+	2.10962i	0.354549	+	0.213104i
$99$	5.21062	−	1.89651i	0.523687	−	0.190606i
$100$	−0.515642	−	2.92435i	−0.0515642	−	0.292435i
$101$	1.00929	+	2.77301i	0.100428	+	0.275925i	0.979724	−	0.200352i	$-0.0642084\pi$
$101$	1.00929	+	2.77301i	0.100428	+	0.275925i	−0.879296	+	0.476276i	$0.841986\pi$
$102$	0.842029	+	1.45844i	0.0833733	+	0.144407i
$103$	8.63421	−	14.9549i	0.850754	−	1.47355i	−0.0297742	−	0.999557i	$-0.509479\pi$
$103$	8.63421	−	14.9549i	0.850754	−	1.47355i	0.880529	−	0.473993i	$-0.157188\pi$
$104$	−7.00762	−	1.23563i	−0.687153	−	0.121164i
$105$	−6.00120	+	3.39475i	−0.585657	+	0.331293i
$106$	3.55628	+	6.15966i	0.345417	+	0.598279i
$107$		−	6.74789i		−	0.652343i	−0.945311	−	0.326171i	$-0.894241\pi$
$107$		−	6.74789i		−	0.652343i	0.945311	−	0.326171i	$-0.105759\pi$
$108$	1.55779	−	0.566988i	0.149898	−	0.0545585i
$109$	−9.29668	−	11.0794i	−0.890461	−	1.06121i	−0.997754	−	0.0669822i	$-0.978663\pi$
$109$	−9.29668	−	11.0794i	−0.890461	−	1.06121i	0.107294	−	0.994227i	$-0.465782\pi$
$110$	−6.47583	−	5.43387i	−0.617446	−	0.518099i
$111$	1.87902	+	2.23932i	0.178348	+	0.212547i
$112$	0.995403	−	5.36855i	0.0940568	−	0.507281i
$113$		−	11.5216i		−	1.08387i	−0.840422	−	0.541933i	$-0.817693\pi$
$113$		−	11.5216i		−	1.08387i	0.840422	−	0.541933i	$-0.182307\pi$
$114$	0.338759	−	2.52740i	0.0317277	−	0.236712i
$115$	−7.76018	−	4.48034i	−0.723641	−	0.417794i
$116$	−0.986364	+	2.71001i	−0.0915816	+	0.251618i
$117$	−3.12483	−	1.13734i	−0.288890	−	0.105147i
$118$	0.764653	+	2.10087i	0.0703920	+	0.193400i
$119$	7.48864	+	1.38850i	0.686483	+	0.127283i
$120$	−4.27177	−	3.58444i	−0.389957	−	0.327213i
$121$	19.7473			1.79521
$122$	−6.60796			−0.598257
$123$	−2.20303	−	1.84856i	−0.198641	−	0.166679i
$124$	1.49037	−	0.542450i	0.133839	−	0.0487135i
$125$	7.24172	−	4.18101i	0.647719	−	0.373961i
$126$	−0.542152	+	1.44973i	−0.0482988	+	0.129153i
$127$	−11.2776	+	13.4402i	−1.00073	+	1.19262i	−0.0194927	+	0.999810i	$0.506205\pi$
$127$	−11.2776	+	13.4402i	−1.00073	+	1.19262i	−0.981236	+	0.192812i	$0.938239\pi$
$128$	11.3358	−	1.99880i	1.00195	−	0.176671i
$129$	−1.79621	+	10.1868i	−0.158148	+	0.896900i
$130$	0.880336	+	4.99263i	0.0772105	+	0.437883i
$131$	−3.72488	−	4.43914i	−0.325445	−	0.387850i	0.578370	−	0.815775i	$-0.303689\pi$
$131$	−3.72488	−	4.43914i	−0.325445	−	0.387850i	−0.903814	+	0.427925i	$0.859245\pi$
$132$	9.19234			0.800090
$133$	−7.69609	−	8.58896i	−0.667335	−	0.744757i
$134$	−2.49469			−0.215508
$135$	−1.67511	−	1.99631i	−0.144170	−	0.171815i
$136$	1.06965	+	6.06630i	0.0917220	+	0.520181i
$137$	−1.68928	+	9.58039i	−0.144325	+	0.818508i	0.823582	+	0.567198i	$0.191973\pi$
$137$	−1.68928	+	9.58039i	−0.144325	+	0.818508i	−0.967907	+	0.251310i	$0.919139\pi$
$138$	−1.98099	+	0.349301i	−0.168633	+	0.0297345i
$139$	−11.7467	+	13.9992i	−0.996344	+	1.18740i	−0.0140785	+	0.999901i	$0.504481\pi$
$139$	−11.7467	+	13.9992i	−0.996344	+	1.18740i	−0.982265	+	0.187496i	$0.939963\pi$
$140$	−11.2734	+	1.88568i	−0.952775	+	0.159369i
$141$	−0.763975	+	0.441081i	−0.0643383	+	0.0371457i
$142$	8.63785	−	3.14392i	0.724873	−	0.263832i
$143$	−14.1253	−	11.8525i	−1.18122	−	0.991158i
$144$	2.06371			0.171976
$145$	4.53355			0.376490
$146$	5.11037	+	4.28811i	0.422938	+	0.354887i
$147$	3.39278	+	6.12283i	0.279832	+	0.505002i
$148$	1.65744	+	4.55377i	0.136240	+	0.374318i
$149$	8.17368	+	2.97498i	0.669614	+	0.243720i	0.654382	−	0.756164i	$-0.272929\pi$
$149$	8.17368	+	2.97498i	0.669614	+	0.243720i	0.0152324	+	0.999884i	$0.495151\pi$
$150$	−0.358402	+	0.984702i	−0.0292634	+	0.0804006i
$151$	1.59951	+	0.923477i	0.130166	+	0.0751515i	0.563669	−	0.826001i	$-0.309389\pi$
$151$	1.59951	+	0.923477i	0.130166	+	0.0751515i	−0.433503	+	0.901152i	$0.642723\pi$
$152$	4.32622	−	8.26331i	0.350903	−	0.670243i
$153$			2.87868i			0.232728i
$154$	−5.57438	+	6.52581i	−0.449196	+	0.525865i
$155$	−1.60261	−	1.90992i	−0.128725	−	0.153408i
$156$	−4.22296	−	3.54348i	−0.338107	−	0.283705i
$157$	14.6076	+	17.4087i	1.16581	+	1.38936i	0.905772	+	0.423765i	$0.139292\pi$
$157$	14.6076	+	17.4087i	1.16581	+	1.38936i	0.260041	+	0.965598i	$0.416264\pi$
$158$	−2.63163	+	0.957835i	−0.209361	+	0.0762012i
$159$			12.1580i			0.964194i
$160$	−7.14950	−	12.3833i	−0.565217	−	0.978985i
$161$	−4.61783	+	7.83822i	−0.363936	+	0.617738i
$162$	−0.576122	−	0.101586i	−0.0452644	−	0.00798134i
$163$	2.74283	−	4.75073i	0.214835	−	0.372106i	−0.738386	−	0.674378i	$-0.764412\pi$
$163$	2.74283	−	4.75073i	0.214835	−	0.372106i	0.953222	+	0.302272i	$0.0977452\pi$
$164$	−2.38374	−	4.12876i	−0.186139	−	0.322402i
$165$	−4.94231	−	13.5789i	−0.384758	−	1.05711i
$166$	−1.22489	−	6.94669i	−0.0950698	−	0.539168i
$167$	−6.79521	+	2.47325i	−0.525829	+	0.191386i	−0.591275	−	0.806470i	$-0.701375\pi$
$167$	−6.79521	+	2.47325i	−0.525829	+	0.191386i	0.0654460	+	0.997856i	$0.479153\pi$
$168$	−3.67713	+	4.30474i	−0.283697	+	0.332118i
$169$	−0.337210	−	1.91241i	−0.0259392	−	0.147109i
$170$	3.80069	−	2.19433i	0.291500	−	0.168297i
$171$	2.66162	−	3.45193i	0.203539	−	0.263975i
$172$	−8.57393	+	14.8505i	−0.653756	+	1.13234i
$173$	−0.432538	+	0.362943i	−0.0328853	+	0.0275940i	−0.659082	−	0.752071i	$-0.729055\pi$
$173$	−0.432538	+	0.362943i	−0.0328853	+	0.0275940i	0.626197	+	0.779665i	$0.284611\pi$
$174$	0.779615	−	0.654175i	0.0591025	−	0.0495929i
$175$	2.33339	+	4.12496i	0.176388	+	0.311817i
$176$	10.7532	+	3.91384i	0.810552	+	0.295017i
$177$	−0.663620	+	3.76358i	−0.0498808	+	0.282888i
$178$	0.855379	−	0.493853i	0.0641134	−	0.0370159i
$179$			15.8953i			1.18807i	0.804438	+	0.594036i	$0.202466\pi$
$179$			15.8953i			1.18807i	−0.804438	+	0.594036i	$0.797534\pi$
$180$	−1.47757	−	4.05960i	−0.110132	−	0.302585i
$181$	−2.07807	+	11.7853i	−0.154462	+	0.875995i	0.804815	+	0.593526i	$0.202265\pi$
$181$	−2.07807	+	11.7853i	−0.154462	+	0.875995i	−0.959276	+	0.282469i	$0.908846\pi$
$182$	5.07645	−	0.849130i	0.376292	−	0.0629417i
$183$	−9.78217	−	5.64774i	−0.723118	−	0.417493i
$184$	−7.24598	−	1.27766i	−0.534180	−	0.0941904i
$185$	5.83568	−	4.89672i	0.429048	−	0.360014i
$186$	−0.551189	−	0.0971894i	−0.0404151	−	0.00712628i
$187$	−5.45945	+	14.9997i	−0.399234	+	1.09689i
$188$	−1.44020	+	0.253946i	−0.105037	+	0.0185209i
$189$	−2.04165	+	1.68276i	−0.148508	+	0.122403i
$190$	−6.58640	−	0.882807i	−0.477828	−	0.0640455i
$191$	10.8808	+	18.8460i	0.787304	+	1.36365i	0.927613	+	0.373543i	$0.121857\pi$
$191$	10.8808	+	18.8460i	0.787304	+	1.36365i	−0.140309	+	0.990108i	$0.544809\pi$
$192$	0.862164	+	0.313802i	0.0622213	+	0.0226467i
$193$	−7.73599	+	1.36406i	−0.556849	+	0.0981874i	−0.444988	−	0.895536i	$-0.646792\pi$
$193$	−7.73599	+	1.36406i	−0.556849	+	0.0981874i	−0.111861	+	0.993724i	$0.535681\pi$
$194$	−2.00085	+	2.38452i	−0.143653	+	0.171199i
$195$	−2.96392	+	8.14330i	−0.212251	+	0.583154i
$196$	1.81366	+	11.4617i	0.129547	+	0.818696i
$197$	9.67909	−	16.7647i	0.689607	−	1.19443i	−0.282358	−	0.959309i	$-0.591117\pi$
$197$	9.67909	−	16.7647i	0.689607	−	1.19443i	0.971965	−	0.235125i	$-0.0755499\pi$
$198$	−2.80929	−	1.62195i	−0.199648	−	0.115267i
$199$	4.59750	−	5.47909i	0.325908	−	0.388402i	−0.578066	−	0.815990i	$-0.696192\pi$
$199$	4.59750	−	5.47909i	0.325908	−	0.388402i	0.903974	+	0.427588i	$0.140637\pi$
$200$	−2.46378	+	2.93622i	−0.174216	+	0.207622i
$201$	−3.69304	−	2.13218i	−0.260487	−	0.150392i
$202$	0.863175	−	1.49506i	0.0607327	−	0.105192i
$203$	0.0404980	−	4.60252i	0.00284240	−	0.323033i
$204$	−1.63218	+	4.48438i	−0.114275	+	0.313969i
$205$	−4.81736	+	5.74111i	−0.336459	+	0.400976i
$206$	−9.94873	+	1.75423i	−0.693161	+	0.122223i
$207$	−3.23111	−	1.17603i	−0.224578	−	0.0817397i
$208$	−3.43129	−	5.94317i	−0.237917	−	0.412085i
$209$	20.4153	−	12.9389i	1.41215	−	0.895001i
$210$	3.77801	+	1.41285i	0.260707	+	0.0974960i
$211$	−13.6724	+	2.41081i	−0.941247	+	0.165967i	−0.623160	−	0.782094i	$-0.714151\pi$
$211$	−13.6724	+	2.41081i	−0.941247	+	0.165967i	−0.318087	+	0.948062i	$0.603040\pi$
$212$	−6.89346	+	18.9396i	−0.473445	+	1.30078i
$213$	15.4742	+	2.72852i	1.06027	+	0.186955i
$214$	−3.02402	+	2.53746i	−0.206718	+	0.173457i
$215$	26.5469	+	4.68093i	1.81048	+	0.319237i
$216$	−1.85315	−	1.06991i	−0.126091	−	0.0727984i
$217$	−1.95329	+	1.60993i	−0.132598	+	0.109289i
$218$	−1.46924	+	8.33250i	−0.0995098	+	0.564348i
$219$	3.90020	+	10.7157i	0.263551	+	0.724101i
$220$		−	23.9552i		−	1.61506i
$221$	8.29019	−	4.78634i	0.557658	−	0.321964i
$222$	0.296959	−	1.68414i	0.0199306	−	0.113032i
$223$	0.836087	+	0.304311i	0.0559885	+	0.0203782i	0.369863	−	0.929086i	$-0.379405\pi$
$223$	0.836087	+	0.304311i	0.0559885	+	0.0203782i	−0.313874	+	0.949465i	$0.601627\pi$
$224$	−12.6355	+	7.14764i	−0.844248	+	0.477572i
$225$	−1.37218	+	1.15139i	−0.0914784	+	0.0767595i
$226$	−5.16335	+	4.33257i	−0.343461	+	0.288198i
$227$	−8.59855	+	14.8931i	−0.570706	+	0.988492i	0.425788	+	0.904823i	$0.359997\pi$
$227$	−8.59855	+	14.8931i	−0.570706	+	0.988492i	−0.996494	+	0.0836687i	$0.973336\pi$
$228$	6.10344	−	3.86826i	0.404210	−	0.256182i
$229$	0.320382	−	0.184973i	0.0211714	−	0.0122233i	−0.489377	−	0.872072i	$-0.662776\pi$
$229$	0.320382	−	0.184973i	0.0211714	−	0.0122233i	0.510548	+	0.859849i	$0.329442\pi$
$230$	0.910280	+	5.16245i	0.0600221	+	0.340402i
$231$	−13.8296	+	4.89620i	−0.909922	+	0.322146i
$232$	3.49806	−	1.27319i	0.229659	−	0.0835891i
$233$	−2.30596	−	13.0778i	−0.151069	−	0.856753i	−0.962292	−	0.272017i	$-0.912309\pi$
$233$	−2.30596	−	13.0778i	−0.151069	−	0.856753i	0.811224	−	0.584736i	$-0.198802\pi$
$234$	0.665357	+	1.82805i	0.0434958	+	0.119504i
$235$	1.14946	+	1.99092i	0.0749824	+	0.129873i
$236$	−3.16769	+	5.48659i	−0.206199	+	0.357147i
$237$	−4.71441	−	0.831277i	−0.306234	−	0.0539972i
$238$	−2.19376	−	3.87811i	−0.142200	−	0.251381i
$239$	8.58755	+	14.8741i	0.555482	+	0.962124i	0.997866	+	0.0652978i	$0.0207997\pi$
$239$	8.58755	+	14.8741i	0.555482	+	0.962124i	−0.442383	+	0.896826i	$0.645867\pi$
$240$		−	5.37802i		−	0.347150i
$241$	22.4505	−	8.17132i	1.44616	−	0.526361i	0.504648	−	0.863325i	$-0.331622\pi$
$241$	22.4505	−	8.17132i	1.44616	−	0.526361i	0.941517	+	0.336964i	$0.109400\pi$
$242$	−7.42571	−	8.84962i	−0.477343	−	0.568875i
$243$	−0.766044	−	0.642788i	−0.0491418	−	0.0412348i
$244$	−12.0363	−	14.3444i	−0.770548	−	0.918303i
$245$	15.9561	−	8.84160i	1.01940	−	0.564869i
$246$			1.68240i			0.107266i
$247$	−14.3665	−	1.92561i	−0.914117	−	0.122523i
$248$	−1.77294	−	1.02361i	−0.112582	−	0.0649993i
$249$	4.12397	−	11.3305i	0.261346	−	0.718041i
$250$	−4.59685	−	1.67312i	−0.290730	−	0.105817i
$251$	5.40238	+	14.8429i	0.340995	+	0.936876i	0.985107	+	0.171945i	$0.0550050\pi$
$251$	5.40238	+	14.8429i	0.340995	+	0.936876i	−0.644112	+	0.764931i	$0.722773\pi$
$252$	−4.13456	+	1.46379i	−0.260453	+	0.0922100i
$253$	−14.6057	−	12.2557i	−0.918256	−	0.770508i
$254$	10.2639			0.644017
$255$	7.50185			0.469784
$256$	−3.75273	−	3.14892i	−0.234546	−	0.196807i
$257$	16.9557	−	6.17137i	1.05767	−	0.384959i	0.246116	−	0.969240i	$-0.420846\pi$
$257$	16.9557	−	6.17137i	1.05767	−	0.384959i	0.811551	+	0.584281i	$0.198623\pi$
$258$	5.24060	−	3.02566i	0.326266	−	0.188370i
$259$	−4.91909	−	5.96821i	−0.305657	−	0.370846i
$260$	−9.23432	+	11.0050i	−0.572688	+	0.682503i
$261$	1.71323	−	0.302088i	0.106046	−	0.0186988i
$262$	−0.588679	+	3.33857i	−0.0363687	+	0.206257i
$263$	−1.94715	−	11.0428i	−0.120066	−	0.680929i	−0.984117	−	0.177524i	$-0.943191\pi$
$263$	−1.94715	−	11.0428i	−0.120066	−	0.680929i	0.864050	−	0.503405i	$-0.167920\pi$
$264$	−7.62693	−	9.08942i	−0.469405	−	0.559415i
$265$	31.6838			1.94632
$266$	−0.955073	+	6.67872i	−0.0585593	+	0.409499i
$267$	1.68836			0.103326
$268$	−4.54405	−	5.41539i	−0.277572	−	0.330797i
$269$	−0.819177	−	4.64578i	−0.0499461	−	0.283258i	0.949597	−	0.313472i	$-0.101492\pi$
$269$	−0.819177	−	4.64578i	−0.0499461	−	0.283258i	−0.999543	+	0.0302138i	$0.990381\pi$
$270$	−0.264733	+	1.50138i	−0.0161111	+	0.0913708i
$271$	−13.5931	+	2.39683i	−0.825722	+	0.145597i	−0.570513	−	0.821289i	$-0.693255\pi$
$271$	−13.5931	+	2.39683i	−0.825722	+	0.145597i	−0.255209	+	0.966886i	$0.582144\pi$
$272$	−3.81864	+	4.55088i	−0.231539	+	0.275938i
$273$	8.24072	+	3.08176i	0.498751	+	0.186516i
$274$	4.92862	−	2.84554i	0.297749	−	0.171905i
$275$	−9.33351	+	3.39712i	−0.562832	+	0.204854i
$276$	−4.36660	−	3.66401i	−0.262838	−	0.220547i
$277$	−20.5333			−1.23372			−0.616862	−	0.787071i	$-0.711596\pi$
$277$	−20.5333			−1.23372			−0.616862	+	0.787071i	$0.711596\pi$
$278$	10.6909			0.641195
$279$	−0.732891	−	0.614969i	−0.0438771	−	0.0368172i
$280$	11.2182	+	9.58261i	0.670413	+	0.572670i
$281$	4.26825	+	11.7269i	0.254622	+	0.699570i	0.999477	+	0.0323424i	$0.0102967\pi$
$281$	4.26825	+	11.7269i	0.254622	+	0.699570i	−0.744854	+	0.667227i	$0.767481\pi$
$282$	0.484951	+	0.176508i	0.0288784	+	0.0105109i
$283$	1.72464	−	4.73841i	0.102519	−	0.281669i	−0.877819	−	0.478992i	$-0.841002\pi$
$283$	1.72464	−	4.73841i	0.102519	−	0.281669i	0.980339	+	0.197323i	$0.0632246\pi$
$284$	22.5585	+	13.0241i	1.33860	+	0.772841i
$285$	−8.99573	−	6.93618i	−0.532861	−	0.410864i
$286$			10.7871i			0.637857i
$287$	5.78542	+	4.94194i	0.341502	+	0.291713i
$288$	−3.52694	−	4.20324i	−0.207827	−	0.247678i
$289$	6.67469	+	5.60073i	0.392629	+	0.329455i
$290$	−1.70478	−	2.03168i	−0.100108	−	0.119304i
$291$	−4.99999	+	1.81985i	−0.293105	+	0.106681i
$292$			18.9042i			1.10628i
$293$	−9.46017	−	16.3855i	−0.552669	−	0.957251i	−0.998081	−	0.0619252i	$-0.980276\pi$
$293$	−9.46017	−	16.3855i	−0.552669	−	0.957251i	0.445412	−	0.895326i	$-0.353057\pi$
$294$	1.46809	−	3.82286i	0.0856210	−	0.222954i
$295$	9.80789	+	1.72940i	0.571038	+	0.100689i
$296$	3.12760	−	5.41717i	0.181788	−	0.314867i
$297$	−2.77251	−	4.80213i	−0.160877	−	0.278648i
$298$	−1.74039	−	4.78168i	−0.100818	−	0.276996i
$299$	1.98553	+	11.2605i	0.114826	+	0.651212i
$300$	−2.79039	+	1.01562i	−0.161103	+	0.0586367i
$301$	4.98929	−	26.9089i	0.287578	−	1.55101i
$302$	−0.187625	−	1.06407i	−0.0107966	−	0.0612304i
$303$	2.55562	−	1.47549i	0.146816	−	0.0847645i
$304$	8.78679	−	1.92642i	0.503957	−	0.110488i
$305$	−14.7180	+	25.4923i	−0.842751	+	1.45969i
$306$	1.29006	−	1.08249i	0.0737480	−	0.0618819i
$307$	−10.7647	+	9.03262i	−0.614372	+	0.515519i	−0.896029	−	0.443996i	$-0.853560\pi$
$307$	−10.7647	+	9.03262i	−0.614372	+	0.515519i	0.281657	+	0.959515i	$0.409116\pi$
$308$	−24.3197	−	0.213991i	−1.38574	−	0.0121933i
$309$	−16.2270	−	5.90615i	−0.923123	−	0.335989i
$310$	−0.253276	+	1.43640i	−0.0143851	+	0.0815820i
$311$	−0.238595	+	0.137753i	−0.0135295	+	0.00781125i	−0.506749	−	0.862093i	$-0.669153\pi$
$311$	−0.238595	+	0.137753i	−0.0135295	+	0.00781125i	0.493220	+	0.869905i	$0.335820\pi$
$312$			7.11572i			0.402848i
$313$	6.54146	+	17.9725i	0.369745	+	1.01587i	0.975458	+	0.220184i	$0.0706657\pi$
$313$	6.54146	+	17.9725i	0.369745	+	1.01587i	−0.605713	+	0.795683i	$0.707112\pi$
$314$	2.30858	−	13.0926i	0.130281	−	0.738858i
$315$	4.38527	+	5.32054i	0.247082	+	0.299778i
$316$	−6.87272	−	3.96797i	−0.386621	−	0.223216i
$317$	−25.7698	−	4.54392i	−1.44738	−	0.255212i	−0.605916	−	0.795528i	$-0.707193\pi$
$317$	−25.7698	−	4.54392i	−1.44738	−	0.255212i	−0.841462	+	0.540317i	$0.818304\pi$
$318$	5.44854	−	4.57187i	0.305539	−	0.256378i
$319$	9.49988	+	1.67508i	0.531891	+	0.0937867i
$320$	0.817769	−	2.24680i	0.0457146	−	0.125600i
$321$	−6.64537	+	1.17176i	−0.370908	+	0.0654012i
$322$	5.24912	−	0.878012i	0.292522	−	0.0489297i
$323$	2.68717	+	12.2568i	0.149518	+	0.681985i
$324$	−0.828882	−	1.43567i	−0.0460490	−	0.0797592i
$325$	5.59734	+	2.03727i	0.310485	+	0.113007i
$326$	−3.16041	+	0.557266i	−0.175039	+	0.0308641i
$327$	−9.29668	+	11.0794i	−0.514108	+	0.612690i
$328$	−2.10474	+	5.78271i	−0.116215	+	0.319297i
$329$	2.03148	−	1.14916i	0.111999	−	0.0633553i
$330$	−4.22680	+	7.32103i	−0.232678	+	0.403009i
$331$	−14.3792	−	8.30182i	−0.790351	−	0.456310i	0.0497349	−	0.998762i	$-0.484162\pi$
$331$	−14.3792	−	8.30182i	−0.790351	−	0.456310i	−0.840086	+	0.542453i	$0.817496\pi$
$332$	12.8485	−	15.3123i	0.705155	−	0.840370i
$333$	1.87902	−	2.23932i	0.102969	−	0.122714i
$334$	3.66362	+	2.11519i	0.200465	+	0.115738i
$335$	−5.55645	+	9.62406i	−0.303582	+	0.525819i
$336$	−5.45984	−	0.0480417i	−0.297859	−	0.00262089i
$337$	7.01207	−	19.2655i	0.381972	−	1.04946i	−0.588554	−	0.808458i	$-0.700302\pi$
$337$	7.01207	−	19.2655i	0.381972	−	1.04946i	0.970525	−	0.241000i	$-0.0774754\pi$
$338$	−0.730231	+	0.870256i	−0.0397194	+	0.0473357i
$339$	−11.3466	+	2.00071i	−0.616263	+	0.108664i
$340$	11.6863	+	4.25346i	0.633778	+	0.230676i
$341$	−2.65252	−	4.59430i	−0.143642	−	0.248795i
$342$	−2.54783	+	0.105266i	−0.137771	+	0.00569211i
$343$	−8.83358	−	16.2778i	−0.476968	−	0.878920i
$344$	21.7980	−	3.84358i	1.17527	−	0.207232i
$345$	−3.06474	+	8.42029i	−0.165000	+	0.453333i
$346$	0.325301	+	0.0573593i	0.0174883	+	0.00308366i
$347$	−4.29713	+	3.60572i	−0.230682	+	0.193565i	−0.750801	−	0.660529i	$-0.770332\pi$
$347$	−4.29713	+	3.60572i	−0.230682	+	0.193565i	0.520119	+	0.854094i	$0.325888\pi$
$348$	2.84012	+	0.500790i	0.152247	+	0.0268452i
$349$	2.37443	+	1.37088i	0.127100	+	0.0733815i	0.562202	−	0.827000i	$-0.309954\pi$
$349$	2.37443	+	1.37088i	0.127100	+	0.0733815i	−0.435102	+	0.900381i	$0.643288\pi$
$350$	0.971130	−	2.59683i	0.0519091	−	0.138807i
$351$	−0.577444	+	3.27485i	−0.0308217	+	0.174799i
$352$	−10.4060	−	28.5904i	−0.554644	−	1.52387i
$353$		−	9.20091i		−	0.489715i	−0.969559	−	0.244857i	$-0.921259\pi$
$353$		−	9.20091i		−	0.489715i	0.969559	−	0.244857i	$-0.0787412\pi$
$354$	1.93617	−	1.11785i	0.102906	−	0.0594130i
$355$	7.11053	−	40.3258i	0.377388	−	2.14027i
$356$	2.63011	+	0.957280i	0.139395	+	0.0507357i
$357$	0.0670138	−	7.61598i	0.00354674	−	0.403081i
$358$	7.12339	−	5.97723i	0.376483	−	0.315907i
$359$	25.8551	−	21.6950i	1.36458	−	1.14502i	0.390043	−	0.920797i	$-0.372460\pi$
$359$	25.8551	−	21.6950i	1.36458	−	1.14502i	0.974538	−	0.224222i	$-0.0719842\pi$
$360$	−2.78820	+	4.82930i	−0.146951	+	0.254527i
$361$	8.11028	−	17.1821i	0.426857	−	0.904319i
$362$	6.06294	−	3.50044i	0.318661	−	0.183979i
$363$	−3.42908	−	19.4473i	−0.179980	−	1.02072i
$364$	11.0900	+	9.47311i	0.581272	+	0.496526i
$365$	27.9252	−	10.1639i	1.46167	−	0.532005i
$366$	1.14746	+	6.50757i	0.0599787	+	0.340156i
$367$	3.91056	+	10.7442i	0.204130	+	0.560842i	0.998941	−	0.0460153i	$-0.0146523\pi$
$367$	3.91056	+	10.7442i	0.204130	+	0.560842i	−0.794811	+	0.606857i	$0.792430\pi$
$368$	−3.54801	−	6.14533i	−0.184953	−	0.320347i
$369$	−1.43793	+	2.49056i	−0.0748555	+	0.129654i
$370$	−4.38887	−	0.773876i	−0.228166	−	0.0402319i
$371$	0.283031	−	32.1659i	0.0146942	−	1.66997i
$372$	−0.793009	−	1.37353i	−0.0411156	−	0.0712143i
$373$		−	16.0441i		−	0.830734i	−0.909654	−	0.415367i	$-0.863653\pi$
$373$		−	16.0441i		−	0.830734i	0.909654	−	0.415367i	$-0.136347\pi$
$374$	8.77498	−	3.19383i	0.453743	−	0.165149i
$375$	−5.37500	−	6.40567i	−0.277564	−	0.330788i
$376$	1.44604	+	1.21337i	0.0745740	+	0.0625750i
$377$	−3.71852	−	4.43156i	−0.191514	−	0.228237i
$378$	1.52185	+	0.282172i	0.0782756	+	0.0145134i
$379$			30.1910i			1.55081i	0.631467	+	0.775403i	$0.282453\pi$
$379$			30.1910i			1.55081i	−0.631467	+	0.775403i	$0.717547\pi$
$380$	−10.0807	−	15.9056i	−0.517129	−	0.815939i
$381$	15.1943	+	8.77244i	0.778429	+	0.449426i
$382$	4.35416	−	11.9630i	0.222778	−	0.612078i
$383$	−20.5241	−	7.47016i	−1.04873	−	0.381707i	−0.240548	−	0.970637i	$-0.577327\pi$
$383$	−20.5241	−	7.47016i	−1.04873	−	0.381707i	−0.808184	+	0.588930i	$0.799549\pi$
$384$	−3.93687	−	10.8165i	−0.200902	−	0.551975i
$385$	12.7595	+	36.0400i	0.650285	+	1.83677i
$386$	3.52032	+	2.95390i	0.179179	+	0.150349i
$387$	10.3440			0.525814
$388$	−8.82076			−0.447806
$389$	−11.4440	−	9.60265i	−0.580234	−	0.486874i	0.304790	−	0.952419i	$-0.401414\pi$
$389$	−11.4440	−	9.60265i	−0.580234	−	0.486874i	−0.885024	+	0.465546i	$0.845858\pi$
$390$	4.76391	−	1.73392i	0.241230	−	0.0878006i
$391$	8.57217	−	4.94915i	0.433513	−	0.250289i
$392$	9.82861	−	11.3032i	0.496420	−	0.570899i
$393$	−3.72488	+	4.43914i	−0.187896	+	0.223925i
$394$	−11.1527	+	1.96652i	−0.561864	+	0.0990718i
$395$	−2.16631	+	12.2858i	−0.108999	+	0.618163i
$396$	−1.59623	−	9.05268i	−0.0802137	−	0.454914i
$397$	14.9909	+	17.8654i	0.752370	+	0.896640i	0.997340	−	0.0728906i	$-0.0232224\pi$
$397$	14.9909	+	17.8654i	0.752370	+	0.896640i	−0.244970	+	0.969531i	$0.578778\pi$
$398$	−4.18425			−0.209737
$399$	−7.12206	+	9.07062i	−0.356549	+	0.454099i
$400$	−3.69661			−0.184831
$401$	6.21904	+	7.41156i	0.310564	+	0.370116i	0.898638	−	0.438692i	$-0.144558\pi$
$401$	6.21904	+	7.41156i	0.310564	+	0.370116i	−0.588074	+	0.808807i	$0.700114\pi$
$402$	0.433198	+	2.45679i	0.0216059	+	0.122533i
$403$	−0.552454	+	3.13312i	−0.0275197	+	0.156072i
$404$	4.81770	−	0.849490i	0.239689	−	0.0422637i
$405$	−1.67511	+	1.99631i	−0.0832367	+	0.0991976i
$406$	−2.07782	+	1.71257i	−0.103120	+	0.0849933i
$407$	14.0377	−	8.10469i	0.695824	−	0.401734i
$408$	5.78840	−	2.10680i	0.286568	−	0.104302i
$409$	27.7902	+	23.3188i	1.37414	+	1.15304i	0.971325	+	0.237758i	$0.0764124\pi$
$409$	27.7902	+	23.3188i	1.37414	+	1.15304i	0.402814	+	0.915282i	$0.368032\pi$
$410$	4.38435			0.216527
$411$	9.72818			0.479856
$412$	−21.9295	−	18.4011i	−1.08039	−	0.906555i
$413$	1.84332	−	9.94166i	0.0907039	−	0.489197i
$414$	0.687989	+	1.89023i	0.0338128	+	0.0928999i
$415$	−29.5273	−	10.7471i	−1.44944	−	0.527553i
$416$	−6.24054	+	17.1457i	−0.305968	+	0.840639i
$417$	15.8263	+	9.13733i	0.775018	+	0.447457i
$418$	−13.4754	−	4.28348i	−0.659102	−	0.209512i
$419$		−	0.310469i		−	0.0151674i	−0.999971	−	0.00758371i	$-0.997586\pi$
$419$		−	0.310469i		−	0.0151674i	0.999971	−	0.00758371i	$-0.00241399\pi$
$420$	3.81464	+	10.7747i	0.186135	+	0.525750i
$421$	−3.27301	−	3.90062i	−0.159517	−	0.190105i	0.680366	−	0.732872i	$-0.261821\pi$
$421$	−3.27301	−	3.90062i	−0.159517	−	0.190105i	−0.839883	+	0.542768i	$0.817376\pi$
$422$	6.22172	+	5.22064i	0.302869	+	0.254137i
$423$	0.567043	+	0.675776i	0.0275706	+	0.0328573i
$424$	24.4471	−	8.89802i	1.18726	−	0.432126i
$425$		−	5.15643i		−	0.250124i
$426$	−4.59611	−	7.96069i	−0.222682	−	0.385697i
$427$	25.7487	+	15.1696i	1.24607	+	0.734111i
$428$	−11.0165	−	1.94250i	−0.532500	−	0.0938942i
$429$	−9.21963	+	15.9689i	−0.445128	+	0.770984i
$430$	−7.88488	−	13.6570i	−0.380243	−	0.658600i
$431$	3.05829	+	8.40259i	0.147313	+	0.404738i	0.991299	−	0.131626i	$-0.0420197\pi$
$431$	3.05829	+	8.40259i	0.147313	+	0.404738i	−0.843987	+	0.536364i	$0.819797\pi$
$432$	−0.358359	−	2.03235i	−0.0172415	−	0.0977817i
$433$	25.7847	−	9.38488i	1.23914	−	0.451009i	0.362419	−	0.932015i	$-0.381951\pi$
$433$	25.7847	−	9.38488i	1.23914	−	0.451009i	0.876717	+	0.481007i	$0.159729\pi$
$434$	1.45599	+	0.269960i	0.0698897	+	0.0129585i
$435$	−0.787242	−	4.46467i	−0.0377454	−	0.214065i
$436$	−20.7641	+	11.9882i	−0.994421	+	0.574129i
$437$	−14.8551	−	1.99110i	−0.710618	−	0.0952474i
$438$	3.33556	−	5.77736i	0.159379	−	0.276053i
$439$	−28.7692	+	24.1402i	−1.37308	+	1.15215i	−0.401383	+	0.915910i	$0.631470\pi$
$439$	−28.7692	+	24.1402i	−1.37308	+	1.15215i	−0.971695	+	0.236239i	$0.924085\pi$
$440$	−23.6870	+	19.8758i	−1.12924	+	0.947541i
$441$	5.44066	−	4.40446i	0.259079	−	0.209736i
$442$	−5.26239	−	1.91535i	−0.250306	−	0.0911040i
$443$	−1.76210	+	9.99339i	−0.0837201	+	0.474800i	0.913905	+	0.405927i	$0.133051\pi$
$443$	−1.76210	+	9.99339i	−0.0837201	+	0.474800i	−0.997625	+	0.0688729i	$0.978060\pi$
$444$	4.19678	−	2.42301i	0.199170	−	0.114991i
$445$		−	4.39987i		−	0.208574i
$446$	−0.178025	−	0.489119i	−0.00842972	−	0.0231605i
$447$	1.51044	−	8.56610i	0.0714411	−	0.405163i
$448$	−2.27368	−	0.850280i	−0.107421	−	0.0401720i
$449$	−9.01880	−	5.20701i	−0.425623	−	0.245734i	0.271857	−	0.962338i	$-0.412362\pi$
$449$	−9.01880	−	5.20701i	−0.425623	−	0.245734i	−0.697480	+	0.716604i	$0.745696\pi$
$450$	1.03198	+	0.181966i	0.0486479	+	0.00857794i
$451$	−12.2159	+	10.2503i	−0.575223	+	0.482669i
$452$	−18.8100	−	3.31671i	−0.884748	−	0.156005i
$453$	0.631696	−	1.73557i	0.0296796	−	0.0815442i
$454$	9.90764	−	1.74698i	0.464988	−	0.0819900i
$455$	8.03106	−	21.4753i	0.376502	−	1.00678i
$456$	−8.88901	−	2.82559i	−0.416266	−	0.132320i
$457$	17.7598	+	30.7608i	0.830767	+	1.43893i	0.897431	+	0.441155i	$0.145431\pi$
$457$	17.7598	+	30.7608i	0.830767	+	1.43893i	−0.0666645	+	0.997775i	$0.521236\pi$
$458$	−0.203370	−	0.0740205i	−0.00950285	−	0.00345875i
$459$	2.83495	−	0.499878i	0.132324	−	0.0233323i
$460$	−9.54842	+	11.3794i	−0.445197	+	0.530565i
$461$	1.27843	−	3.51247i	0.0595426	−	0.163592i	−0.906355	−	0.422518i	$-0.861146\pi$
$461$	1.27843	−	3.51247i	0.0595426	−	0.163592i	0.965897	+	0.258926i	$0.0833686\pi$
$462$	7.39465	+	4.35650i	0.344030	+	0.202683i
$463$	13.3703	−	23.1580i	0.621369	−	1.07624i	−0.367862	−	0.929881i	$-0.619910\pi$
$463$	13.3703	−	23.1580i	0.621369	−	1.07624i	0.989231	−	0.146363i	$-0.0467567\pi$
$464$	3.10915	+	1.79507i	0.144339	+	0.0833340i
$465$	−1.60261	+	1.90992i	−0.0743193	+	0.0885703i
$466$	−4.99359	+	5.95113i	−0.231324	+	0.275681i
$467$	23.0555	+	13.3111i	1.06688	+	0.615966i	0.927328	−	0.374249i	$-0.122099\pi$
$467$	23.0555	+	13.3111i	1.06688	+	0.615966i	0.139555	+	0.990214i	$0.455433\pi$
$468$	−2.75634	+	4.77412i	−0.127412	+	0.220684i
$469$	9.72084	+	5.72696i	0.448867	+	0.264446i
$470$	0.459979	−	1.26378i	0.0212173	−	0.0582940i
$471$	14.6076	−	17.4087i	0.673083	−	0.802149i
$472$	8.05341	−	1.42003i	0.370688	−	0.0653623i
$473$	53.8985	+	19.6174i	2.47825	+	0.902011i
$474$	1.40026	+	2.42532i	0.0643161	+	0.111399i
$475$	−4.76762	+	6.18326i	−0.218753	+	0.283707i
$476$	4.42257	−	11.8261i	0.202708	−	0.542048i
$477$	11.9733	−	2.11122i	0.548220	−	0.0966660i
$478$	3.43648	−	9.44166i	0.157181	−	0.431851i
$479$	−37.2165	−	6.56227i	−1.70046	−	0.299838i	−0.762608	−	0.646861i	$-0.776081\pi$
$479$	−37.2165	−	6.56227i	−1.70046	−	0.299838i	−0.937857	+	0.347023i	$0.887193\pi$
$480$	−10.9537	+	9.19121i	−0.499964	+	0.419520i
$481$	−9.57314	−	1.68800i	−0.436498	−	0.0769663i
$482$	−12.1042	−	6.98834i	−0.551329	−	0.318310i
$483$	8.52102	+	3.18658i	0.387720	+	0.144994i
$484$	5.68460	−	32.2390i	0.258391	−	1.46541i
$485$	4.74253	+	13.0300i	0.215347	+	0.591662i
$486$			0.585010i			0.0265366i
$487$	−12.5258	+	7.23179i	−0.567599	+	0.327704i	−0.756190	−	0.654352i	$-0.772941\pi$
$487$	−12.5258	+	7.23179i	−0.567599	+	0.327704i	0.188591	+	0.982056i	$0.439608\pi$
$488$	−4.19714	+	23.8032i	−0.189996	+	1.07752i
$489$	−5.15484	−	1.87621i	−0.233110	−	0.0848451i
$490$	−9.96239	−	3.82586i	−0.450055	−	0.172835i
$491$	18.9556	−	15.9056i	0.855454	−	0.717811i	−0.105530	−	0.994416i	$-0.533654\pi$
$491$	18.9556	−	15.9056i	0.855454	−	0.717811i	0.960984	+	0.276605i	$0.0892093\pi$
$492$	−3.65211	+	3.06448i	−0.164650	+	0.138157i
$493$	−2.50396	+	4.33698i	−0.112773	+	0.195328i
$494$	4.53938	+	7.16234i	0.204236	+	0.322249i
$495$	−12.5144	+	7.22517i	−0.562479	+	0.324747i
$496$	−0.342850	−	1.94440i	−0.0153944	−	0.0873060i
$497$	−40.8758	−	7.57893i	−1.83353	−	0.339962i
$498$	−6.62846	+	2.41256i	−0.297028	+	0.108109i
$499$	0.972034	+	5.51268i	0.0435142	+	0.246781i	0.998804	−	0.0488891i	$-0.0155681\pi$
$499$	0.972034	+	5.51268i	0.0435142	+	0.246781i	−0.955290	+	0.295670i	$0.904457\pi$
$500$	−4.74117	−	13.0262i	−0.212031	−	0.582551i
$501$	3.61565	+	6.26250i	0.161536	+	0.279788i
$502$	4.62026	−	8.00253i	0.206212	−	0.357170i
$503$	−19.0937	−	3.36674i	−0.851346	−	0.150115i	−0.269084	−	0.963117i	$-0.586721\pi$
$503$	−19.0937	−	3.36674i	−0.851346	−	0.150115i	−0.582262	+	0.813001i	$0.697832\pi$
$504$	4.87787	+	2.87376i	0.217277	+	0.128007i
$505$	−3.84512	−	6.65995i	−0.171106	−	0.296364i
$506$			11.1541i			0.495859i
$507$	−1.82480	+	0.664173i	−0.0810423	+	0.0294970i
$508$	18.6957	+	22.2806i	0.829486	+	0.988542i
$509$	−19.8857	−	16.6861i	−0.881419	−	0.739599i	0.0850511	−	0.996377i	$-0.472895\pi$
$509$	−19.8857	−	16.6861i	−0.881419	−	0.739599i	−0.966470	+	0.256778i	$0.917339\pi$
$510$	−2.82098	−	3.36191i	−0.124915	−	0.148868i
$511$	−10.0691	−	28.4408i	−0.445431	−	1.25815i
$512$		−	20.1554i		−	0.890751i
$513$	−3.86167	−	2.02176i	−0.170497	−	0.0892629i
$514$	−9.14163	−	5.27792i	−0.403220	−	0.232799i
$515$	−15.3914	+	42.2876i	−0.678228	+	1.86342i
$516$	16.1137	+	5.86491i	0.709367	+	0.258188i
$517$	1.67303	+	4.59661i	0.0735798	+	0.202159i
$518$	−0.824855	+	4.44872i	−0.0362420	+	0.195466i
$519$	0.432538	+	0.362943i	0.0189863	+	0.0159314i
$520$	18.5436			0.813190
$521$	−40.1874			−1.76064			−0.880321	−	0.474378i	$-0.842673\pi$
$521$	−40.1874			−1.76064			−0.880321	+	0.474378i	$0.842673\pi$
$522$	−0.779615	−	0.654175i	−0.0341228	−	0.0286325i
$523$	−36.2414	+	13.1908i	−1.58473	+	0.576793i	−0.976225	−	0.216760i	$-0.930451\pi$
$523$	−36.2414	+	13.1908i	−1.58473	+	0.576793i	−0.608501	+	0.793553i	$0.708229\pi$
$524$	−8.31952	+	4.80328i	−0.363440	+	0.209832i
$525$	3.65710	−	3.01424i	0.159609	−	0.131552i
$526$	−4.21657	+	5.02511i	−0.183851	+	0.219105i
$527$	2.71226	−	0.478244i	0.118148	−	0.0208326i
$528$	1.98711	−	11.2694i	0.0864778	−	0.490440i
$529$	−1.94084	−	11.0071i	−0.0843844	−	0.478567i
$530$	−11.9143	−	14.1989i	−0.517524	−	0.616761i
$531$	3.82164			0.165845
$532$	−16.2376	+	10.0920i	−0.703989	+	0.437543i
$533$	9.56328			0.414232
$534$	−0.634886	−	0.756627i	−0.0274742	−	0.0327425i
$535$	3.05360	+	17.3179i	0.132019	+	0.748716i
$536$	−1.58454	+	8.98635i	−0.0684415	+	0.388151i
$537$	15.6538	−	2.76019i	0.675513	−	0.119111i
$538$	−1.77394	+	2.11410i	−0.0764799	+	0.0911452i
$539$	36.7023	−	12.6317i	1.58088	−	0.544085i
$540$	−3.74135	+	2.16007i	−0.161002	+	0.0929545i
$541$	−33.5118	+	12.1973i	−1.44079	+	0.524403i	−0.940002	−	0.341168i	$-0.889177\pi$
$541$	−33.5118	+	12.1973i	−1.44079	+	0.524403i	−0.500785	+	0.865572i	$0.666955\pi$
$542$	6.18563	+	5.19036i	0.265696	+	0.222945i
$543$	11.9671			0.513558
$544$	15.7952			0.677212
$545$	28.8728	+	24.2272i	1.23678	+	1.03778i
$546$	−1.71775	−	4.85188i	−0.0735127	−	0.207641i
$547$	10.9242	+	30.0140i	0.467084	+	1.28330i	0.920059	+	0.391780i	$0.128141\pi$
$547$	10.9242	+	30.0140i	0.467084	+	1.28330i	−0.452974	+	0.891524i	$0.649637\pi$
$548$	15.1544	+	5.51577i	0.647366	+	0.235622i
$549$	−3.86328	+	10.6143i	−0.164881	+	0.453006i
$550$	5.03214	+	2.90531i	0.214571	+	0.123883i
$551$	7.01253	−	2.88547i	0.298744	−	0.122925i
$552$			7.35776i			0.313167i
$553$	12.4533	+	2.30902i	0.529569	+	0.0981893i
$554$	7.72127	+	9.20185i	0.328045	+	0.390949i
$555$	−5.83568	−	4.89672i	−0.247711	−	0.207854i
$556$	19.4733	+	23.2074i	0.825851	+	0.984211i
$557$	4.57210	−	1.66411i	0.193726	−	0.0705106i	−0.243335	−	0.969942i	$-0.578241\pi$
$557$	4.57210	−	1.66411i	0.193726	−	0.0705106i	0.437061	+	0.899432i	$0.356019\pi$
$558$			0.559692i			0.0236936i
$559$	−17.1988	−	29.7891i	−0.727430	−	1.25995i
$560$	−0.125197	+	14.2284i	−0.00529053	+	0.601258i
$561$	15.7199	+	2.77183i	0.663693	+	0.117027i
$562$	3.65032	−	6.32255i	0.153980	−	0.266701i
$563$	−15.0516	−	26.0701i	−0.634349	−	1.09872i	−0.986653	−	0.162839i	$-0.947935\pi$
$563$	−15.0516	−	26.0701i	−0.634349	−	1.09872i	0.352303	−	0.935886i	$-0.385398\pi$
$564$	0.500176	+	1.37422i	0.0210612	+	0.0578652i
$565$	5.21386	+	29.5693i	0.219349	+	1.24399i
$566$	−2.77201	+	1.00893i	−0.116516	+	0.0424085i
$567$	2.01172	+	1.71842i	0.0844843	+	0.0721670i
$568$	−5.83856	−	33.1121i	−0.244981	−	1.38935i
$569$	−27.8634	+	16.0869i	−1.16809	+	0.674399i	−0.953230	−	0.302245i	$-0.902264\pi$
$569$	−27.8634	+	16.0869i	−1.16809	+	0.674399i	−0.214863	+	0.976644i	$0.568931\pi$
$570$	0.274322	+	6.63964i	0.0114901	+	0.278104i
$571$	6.81032	−	11.7958i	0.285003	−	0.493640i	−0.687607	−	0.726083i	$-0.741339\pi$
$571$	6.81032	−	11.7958i	0.285003	−	0.493640i	0.972610	+	0.232443i	$0.0746720\pi$
$572$	−23.4164	+	19.6487i	−0.979088	+	0.821553i
$573$	16.6703	−	13.9880i	0.696412	−	0.584359i
$574$	0.0391652	−	4.45105i	0.00163472	−	0.185783i
$575$	5.78773	+	2.10656i	0.241365	+	0.0878497i
$576$	0.159321	−	0.903557i	0.00663839	−	0.0376482i
$577$	−17.2682	+	9.96979i	−0.718884	+	0.415048i	−0.814342	−	0.580386i	$-0.802902\pi$
$577$	−17.2682	+	9.96979i	−0.718884	+	0.415048i	0.0954578	+	0.995433i	$0.469568\pi$
$578$		−	5.09730i		−	0.212020i
$579$	2.68668	+	7.38159i	0.111655	+	0.306769i
$580$	1.30506	−	7.40137i	0.0541897	−	0.307325i
$581$	−11.1743	+	29.8805i	−0.463589	+	1.23965i
$582$	2.69574	+	1.55638i	0.111742	+	0.0645142i
$583$	66.3923	+	11.7068i	2.74969	+	0.484844i
$584$	18.6925	−	15.6849i	0.773503	−	0.649046i
$585$	8.53427	+	1.50482i	0.352849	+	0.0622167i
$586$	−3.78568	+	10.4011i	−0.156385	+	0.429664i
$587$	9.68672	−	1.70803i	0.399814	−	0.0704980i	0.0298740	−	0.999554i	$-0.490489\pi$
$587$	9.68672	−	1.70803i	0.399814	−	0.0704980i	0.369940	+	0.929056i	$0.379378\pi$
$588$	10.9727	−	3.77642i	0.452505	−	0.155737i
$589$	−3.69454	−	1.93426i	−0.152231	−	0.0796999i
$590$	−2.91311	−	5.04566i	−0.119931	−	0.207727i
$591$	−18.1907	−	6.62089i	−0.748267	−	0.272347i
$592$	5.94104	−	1.04756i	0.244175	−	0.0430547i
$593$	−4.52478	+	5.39242i	−0.185810	+	0.221440i	−0.850906	−	0.525318i	$-0.823946\pi$
$593$	−4.52478	+	5.39242i	−0.185810	+	0.221440i	0.665096	+	0.746758i	$0.268391\pi$
$594$	−1.10948	+	3.04826i	−0.0455224	+	0.125072i
$595$	−19.8473	−	0.174638i	−0.813659	−	0.00715946i
$596$	7.20982	−	12.4878i	0.295326	−	0.511519i
$597$	−6.19419	−	3.57622i	−0.253511	−	0.146365i
$598$	4.29969	−	5.12417i	0.175827	−	0.209543i
$599$	−9.79721	+	11.6759i	−0.400303	+	0.477063i	−0.928112	−	0.372300i	$-0.878569\pi$
$599$	−9.79721	+	11.6759i	−0.400303	+	0.477063i	0.527809	+	0.849363i	$0.323014\pi$
$600$	3.31944	+	1.91648i	0.135516	+	0.0782400i
$601$	0.600997	−	1.04096i	0.0245152	−	0.0424615i	−0.853508	−	0.521080i	$-0.825529\pi$
$601$	0.600997	−	1.04096i	0.0245152	−	0.0424615i	0.878023	+	0.478619i	$0.158862\pi$
$602$	−13.9352	+	7.88284i	−0.567957	+	0.321281i
$603$	−1.45849	+	4.00718i	−0.0593945	+	0.163185i
$604$	1.96810	−	2.34548i	0.0800807	−	0.0954364i
$605$	−50.6796	+	8.93619i	−2.06042	+	0.363308i
$606$	−1.62224	−	0.590446i	−0.0658989	−	0.0239852i
$607$	−17.9552	−	31.0993i	−0.728777	−	1.26228i	−0.957400	−	0.288765i	$-0.906756\pi$
$607$	−17.9552	−	31.0993i	−0.728777	−	1.26228i	0.228623	−	0.973515i	$-0.426578\pi$
$608$	−18.9405	−	14.6041i	−0.768140	−	0.592276i
$609$	−4.53963	+	0.759336i	−0.183955	+	0.0307698i
$610$	16.9588	−	2.99029i	0.686640	−	0.121073i
$611$	1.00332	−	2.75660i	0.0405901	−	0.111520i
$612$	4.69967	+	0.828679i	0.189973	+	0.0334974i
$613$	−7.06242	+	5.92607i	−0.285248	+	0.239352i	−0.774173	−	0.632974i	$-0.781834\pi$
$613$	−7.06242	+	5.92607i	−0.285248	+	0.239352i	0.488924	+	0.872326i	$0.337389\pi$
$614$	8.09582	+	1.42751i	0.326721	+	0.0576097i
$615$	6.49041	+	3.74724i	0.261719	+	0.151103i
$616$	19.9666	+	24.2250i	0.804476	+	0.976052i
$617$	2.86240	−	16.2335i	0.115236	−	0.653536i	−0.871397	−	0.490578i	$-0.836785\pi$
$617$	2.86240	−	16.2335i	0.115236	−	0.653536i	0.986633	−	0.162958i	$-0.0521034\pi$
$618$	3.45516	+	9.49296i	0.138987	+	0.381863i
$619$			4.60072i			0.184919i	0.995716	+	0.0924594i	$0.0294728\pi$
$619$			4.60072i			0.184919i	−0.995716	+	0.0924594i	$0.970527\pi$
$620$	−3.57943	+	2.06658i	−0.143753	+	0.0829960i
$621$	−0.597086	+	3.38624i	−0.0239602	+	0.135885i
$622$	0.151454	+	0.0551246i	0.00607274	+	0.00221030i
$623$	−4.46680	−	0.0393038i	−0.178959	−	0.00157468i
$624$	−5.25705	+	4.41119i	−0.210450	+	0.176589i
$625$	−23.5541	+	19.7642i	−0.942163	+	0.790569i
$626$	5.59444	−	9.68985i	0.223599	−	0.387284i
$627$	−16.2874	−	17.8583i	−0.650456	−	0.713192i
$628$	32.6261	−	18.8367i	1.30192	−	0.751665i
$629$	1.46126	+	8.28720i	0.0582642	+	0.330432i
$630$	0.735342	−	3.96595i	0.0292967	−	0.158007i
$631$	−20.6971	+	7.53313i	−0.823938	+	0.299889i	−0.719369	−	0.694629i	$-0.755569\pi$
$631$	−20.6971	+	7.53313i	−0.823938	+	0.299889i	−0.104570	+	0.994518i	$0.533347\pi$
$632$	1.77879	+	10.0880i	0.0707565	+	0.401280i
$633$	4.74837	+	13.0460i	0.188731	+	0.518534i
$634$	7.65409	+	13.2573i	0.303983	+	0.526513i
$635$	22.8610	−	39.5964i	0.907212	−	1.57134i
$636$	19.8489	+	3.49990i	0.787061	+	0.138780i
$637$	−21.7303	−	8.34508i	−0.860986	−	0.330644i
$638$	−2.82163	−	4.88720i	−0.111709	−	0.193486i
$639$		−	15.7129i		−	0.621593i
$640$	−28.1877	+	10.2595i	−1.11422	+	0.405542i
$641$	−11.5441	−	13.7577i	−0.455965	−	0.543398i	0.488260	−	0.872698i	$-0.337632\pi$
$641$	−11.5441	−	13.7577i	−0.455965	−	0.543398i	−0.944225	+	0.329300i	$0.893187\pi$
$642$	3.02402	+	2.53746i	0.119349	+	0.100145i
$643$	−15.5755	−	18.5622i	−0.614238	−	0.732020i	0.365830	−	0.930682i	$-0.380785\pi$
$643$	−15.5755	−	18.5622i	−0.614238	−	0.732020i	−0.980068	+	0.198661i	$0.936341\pi$
$644$	11.4672	+	9.79533i	0.451870	+	0.385990i
$645$		−	26.9564i		−	1.06141i
$646$	4.48232	−	5.81324i	0.176354	−	0.228719i
$647$	36.7035	+	21.1908i	1.44296	+	0.833096i	0.998047	−	0.0624750i	$-0.0198994\pi$
$647$	36.7035	+	21.1908i	1.44296	+	0.833096i	0.444918	+	0.895571i	$0.353233\pi$
$648$	−0.731864	+	2.01078i	−0.0287503	+	0.0789909i
$649$	19.9131	+	7.24777i	0.781657	+	0.284500i
$650$	−1.19182	−	3.27450i	−0.0467470	−	0.128436i
$651$	1.92466	+	1.64405i	0.0754333	+	0.0644355i
$652$	−6.96636	−	5.84547i	−0.272824	−	0.228926i
$653$	−25.6486			−1.00371			−0.501854	−	0.864953i	$-0.667348\pi$
$653$	−25.6486			−1.00371			−0.501854	+	0.864953i	$0.667348\pi$
$654$	8.46104			0.330853
$655$	11.5684	+	9.70706i	0.452016	+	0.379286i
$656$	−5.57700	+	2.02986i	−0.217745	+	0.0792528i
$657$	9.87566	−	5.70171i	0.385286	−	0.222445i
$658$	−1.27890	−	0.478267i	−0.0498567	−	0.0186448i
$659$	22.5272	−	26.8469i	0.877536	−	1.04581i	−0.121050	−	0.992646i	$-0.538626\pi$
$659$	22.5272	−	26.8469i	0.877536	−	1.04581i	0.998586	−	0.0531603i	$-0.0169294\pi$
$660$	−23.5913	+	4.15979i	−0.918291	+	0.161919i
$661$	−0.0658486	+	0.373446i	−0.00256121	+	0.0145254i	−0.986062	−	0.166381i	$-0.946792\pi$
$661$	−0.0658486	+	0.373446i	−0.00256121	+	0.0145254i	0.983500	+	0.180906i	$0.0579030\pi$
$662$	1.68670	+	9.56573i	0.0655553	+	0.371783i
$663$	−6.15320	−	7.33310i	−0.238971	−	0.284794i
$664$	−25.8013			−1.00129
$665$	23.6381	+	18.5601i	0.916645	+	0.719730i
$666$	−1.71012			−0.0662657
$667$	−3.84501	−	4.58230i	−0.148879	−	0.177427i
$668$	2.08166	+	11.8057i	0.0805418	+	0.456775i
$669$	0.154503	−	0.876228i	0.00597342	−	0.0338769i
$670$	6.40239	−	1.12891i	0.247346	−	0.0436138i
$671$	−40.2601	+	47.9802i	−1.55423	+	1.85225i
$672$	9.23320	+	11.2024i	0.356178	+	0.432142i
$673$	−32.8330	+	18.9561i	−1.26562	+	0.730706i	−0.974156	−	0.225876i	$-0.927476\pi$
$673$	−32.8330	+	18.9561i	−1.26562	+	0.730706i	−0.291464	+	0.956582i	$0.594142\pi$
$674$	−11.2705	+	4.10213i	−0.434124	+	0.158008i
$675$	1.37218	+	1.15139i	0.0528151	+	0.0443171i
$676$	−3.21923			−0.123817
$677$	−19.7586			−0.759384			−0.379692	−	0.925113i	$-0.623970\pi$
$677$	−19.7586			−0.759384			−0.379692	+	0.925113i	$0.623970\pi$
$678$	5.16335	+	4.33257i	0.198297	+	0.166391i
$679$	13.2706	−	4.69828i	0.509279	−	0.180304i
$680$	−5.49034	−	15.0846i	−0.210545	−	0.578467i
$681$	16.1600	+	5.88176i	0.619252	+	0.225389i
$682$	−1.06146	+	2.91634i	−0.0406454	+	0.111672i
$683$	−34.9748	−	20.1927i	−1.33827	−	0.772653i	−0.351723	−	0.936104i	$-0.614404\pi$
$683$	−34.9748	−	20.1927i	−1.33827	−	0.772653i	−0.986551	+	0.163452i	$0.947737\pi$
$684$	−4.86935	−	5.33900i	−0.186184	−	0.204142i
$685$		−	25.3517i		−	0.968637i
$686$	−3.97305	+	10.0798i	−0.151692	+	0.384848i
$687$	−0.237796	−	0.283394i	−0.00907249	−	0.0108122i
$688$	16.3527	+	13.7215i	0.623440	+	0.523129i
$689$	−25.9879	−	30.9711i	−0.990058	−	1.17991i
$690$	4.92595	−	1.79290i	0.187528	−	0.0682546i
$691$			35.4999i			1.35048i	0.737599	+	0.675239i	$0.235960\pi$
$691$			35.4999i			1.35048i	−0.737599	+	0.675239i	$0.764040\pi$
$692$	0.468019	+	0.810632i	0.0177914	+	0.0308156i
$693$	7.22330	+	12.7693i	0.274391	+	0.485065i
$694$	3.23176	+	0.569847i	0.122676	+	0.0216311i
$695$	23.8119	−	41.2434i	0.903237	−	1.56445i
$696$	−1.86128	−	3.22383i	−0.0705517	−	0.122199i
$697$	−2.83147	−	7.77941i	−0.107250	−	0.294666i
$698$	−0.278524	−	1.57959i	−0.0105423	−	0.0597883i
$699$	−12.4787	+	4.54186i	−0.471986	+	0.171789i
$700$	7.40602	−	2.62201i	0.279921	−	0.0991026i
$701$	4.29238	+	24.3433i	0.162121	+	0.919434i	0.951983	+	0.306150i	$0.0990409\pi$
$701$	4.29238	+	24.3433i	0.162121	+	0.919434i	−0.789862	+	0.613284i	$0.789848\pi$
$702$	1.68474	−	0.972687i	0.0635866	−	0.0367117i
$703$	5.91007	−	11.2885i	0.222903	−	0.425755i
$704$	2.54377	−	4.40593i	0.0958718	−	0.166055i
$705$	1.76107	−	1.47772i	0.0663259	−	0.0556540i
$706$	−4.12333	+	3.45988i	−0.155184	+	0.130214i
$707$	−6.79562	+	3.84413i	−0.255575	+	0.144573i
$708$	5.95330	+	2.16682i	0.223739	+	0.0814343i
$709$	7.89880	−	44.7963i	0.296646	−	1.68236i	−0.363792	−	0.931480i	$-0.618518\pi$
$709$	7.89880	−	44.7963i	0.296646	−	1.68236i	0.660438	−	0.750881i	$-0.270371\pi$
$710$	−20.7456	+	11.9775i	−0.778568	+	0.449506i
$711$			4.78713i			0.179532i
$712$	−1.23565	−	3.39492i	−0.0463079	−	0.127230i
$713$	−0.571245	+	3.23969i	−0.0213933	+	0.121327i
$714$	−3.43825	+	2.83386i	−0.128673	+	0.106055i
$715$	41.6149	+	24.0264i	1.55631	+	0.898535i
$716$	25.9504	+	4.57575i	0.969810	+	0.171004i
$717$	13.1569	−	11.0399i	0.491353	−	0.412294i
$718$	−19.4450	−	3.42867i	−0.725680	−	0.127957i
$719$	−11.6538	+	32.0184i	−0.434612	+	1.19409i	0.508340	+	0.861157i	$0.330259\pi$
$719$	−11.6538	+	32.0184i	−0.434612	+	1.19409i	−0.942952	+	0.332930i	$0.891963\pi$
$720$	−5.29632	+	0.933884i	−0.197382	+	0.0348038i
$721$	42.7935	+	16.0034i	1.59371	+	0.595996i
$722$	−10.7498	+	2.82653i	−0.400066	+	0.105192i
$723$	−11.9457	−	20.6905i	−0.444264	−	0.769488i
$724$	18.6422	+	6.78522i	0.692833	+	0.252171i
$725$	−3.06881	+	0.541115i	−0.113973	+	0.0200965i
$726$	−7.42571	+	8.84962i	−0.275594	+	0.328440i
$727$	−5.56117	+	15.2792i	−0.206252	+	0.566673i	−0.999085	−	0.0427657i	$-0.986383\pi$
$727$	−5.56117	+	15.2792i	−0.206252	+	0.566673i	0.792833	+	0.609439i	$0.208605\pi$
$728$	0.165649	−	18.8257i	0.00613937	−	0.697727i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	−15.0558	−	8.69248i	−0.557241	−	0.321723i
$731$	−19.1403	+	22.8105i	−0.707929	+	0.843677i
$732$	−12.0363	+	14.3444i	−0.444876	+	0.530182i
$733$	6.59487	+	3.80755i	0.243587	+	0.140635i	0.616824	−	0.787101i	$-0.288419\pi$
$733$	6.59487	+	3.80755i	0.243587	+	0.140635i	−0.373237	+	0.927736i	$0.621752\pi$
$734$	3.34442	−	5.79270i	0.123445	−	0.213813i
$735$	−11.4780	−	14.1784i	−0.423373	−	0.522977i
$736$	−6.45281	+	17.7289i	−0.237854	+	0.653498i
$737$	−15.1993	+	18.1138i	−0.559874	+	0.667231i
$738$	1.65684	−	0.292146i	0.0609893	−	0.0107541i
$739$	−10.7880	−	3.92651i	−0.396843	−	0.144439i	0.135887	−	0.990724i	$-0.456612\pi$
$739$	−10.7880	−	3.92651i	−0.396843	−	0.144439i	−0.532730	+	0.846285i	$0.678834\pi$
$740$	−6.31437	−	10.9368i	−0.232121	−	0.402045i
$741$	0.598361	+	14.4826i	0.0219813	+	0.532031i
$742$	−14.5214	+	11.9687i	−0.533096	+	0.439385i
$743$	−31.8293	+	5.61237i	−1.16771	+	0.205898i	−0.723693	−	0.690123i	$-0.757557\pi$
$743$	−31.8293	+	5.61237i	−1.16771	+	0.205898i	−0.444013	+	0.896020i	$0.646445\pi$
$744$	−0.700190	+	1.92376i	−0.0256702	+	0.0705284i
$745$	−22.3233	−	3.93620i	−0.817862	−	0.144211i
$746$	−7.19008	+	6.03319i	−0.263248	+	0.220891i
$747$	−11.8745	−	2.09379i	−0.434465	−	0.0766078i
$748$	22.9166	+	13.2309i	0.837914	+	0.483770i
$749$	17.6086	−	2.94536i	0.643404	−	0.107621i
$750$	−0.849463	+	4.81754i	−0.0310180	+	0.175912i
$751$	14.2702	+	39.2070i	0.520727	+	1.43068i	0.869713	+	0.493557i	$0.164304\pi$
$751$	14.2702	+	39.2070i	0.520727	+	1.43068i	−0.348987	+	0.937128i	$0.613474\pi$
$752$			1.82052i			0.0663877i
$753$	13.6793	−	7.89775i	0.498501	−	0.287810i
$754$	−0.587674	+	3.33287i	−0.0214018	+	0.121376i
$755$	−4.52290	−	1.64620i	−0.164605	−	0.0599114i
$756$	2.15951	+	3.81756i	0.0785406	+	0.138843i
$757$	11.9256	−	10.0068i	0.433445	−	0.363704i	−0.399805	−	0.916600i	$-0.630922\pi$
$757$	11.9256	−	10.0068i	0.433445	−	0.363704i	0.833250	+	0.552897i	$0.186478\pi$
$758$	13.5299	−	11.3529i	0.491428	−	0.412357i
$759$	−9.53323	+	16.5120i	−0.346034	+	0.599349i
$760$	−7.36349	+	23.1648i	−0.267102	+	0.840275i
$761$	−13.6391	+	7.87454i	−0.494417	+	0.285452i	−0.726405	−	0.687267i	$-0.758810\pi$
$761$	−13.6391	+	7.87454i	−0.494417	+	0.285452i	0.231988	+	0.972719i	$0.425477\pi$
$762$	−1.78231	−	10.1080i	−0.0645664	−	0.366174i
$763$	24.8537	−	29.0957i	0.899763	−	1.05333i
$764$	33.8998	−	12.3385i	1.22645	−	0.446392i
$765$	−1.30268	−	7.38788i	−0.0470986	−	0.267109i
$766$	4.37012	+	12.0068i	0.157899	+	0.433823i
$767$	−6.35418	−	11.0058i	−0.229436	−	0.397395i
$768$	−2.44942	+	4.24252i	−0.0883859	+	0.153089i
$769$	−34.1830	−	6.02739i	−1.23267	−	0.217353i	−0.480899	−	0.876776i	$-0.659689\pi$
$769$	−34.1830	−	6.02739i	−1.23267	−	0.217353i	−0.751772	+	0.659423i	$0.770801\pi$
$770$	11.3530	−	19.2705i	0.409135	−	0.694460i
$771$	−9.02193	−	15.6264i	−0.324917	−	0.562773i
$772$			13.0223i			0.468682i
$773$	17.5922	−	6.40302i	0.632746	−	0.230301i	−0.00568011	−	0.999984i	$-0.501808\pi$
$773$	17.5922	−	6.40302i	0.632746	−	0.230301i	0.638426	+	0.769683i	$0.279586\pi$
$774$	−3.88972	−	4.63558i	−0.139813	−	0.166623i
$775$	1.31279	+	1.10156i	0.0471568	+	0.0395693i
$776$	7.31863	+	8.72201i	0.262724	+	0.313102i
$777$	−5.02335	+	5.88072i	−0.180211	+	0.210970i
$778$			8.73951i			0.313326i
$779$	−3.79749	+	11.9465i	−0.136059	+	0.428028i
$780$	12.4414	+	7.18302i	0.445472	+	0.257194i
$781$	29.7997	−	81.8740i	1.06632	−	2.92968i
$782$	−5.44138	−	1.98050i	−0.194583	−	0.0708226i
$783$	−0.594997	−	1.63474i	−0.0212635	−	0.0584209i
$784$	14.4437	+	0.254203i	0.515847	+	0.00907867i
$785$	−45.3670	−	38.0674i	−1.61922	−	1.35869i
$786$	3.39007			0.120920
$787$	20.3652			0.725942			0.362971	−	0.931801i	$-0.381762\pi$
$787$	20.3652			0.725942			0.362971	+	0.931801i	$0.381762\pi$
$788$	−24.5834	−	20.6279i	−0.875746	−	0.734838i
$789$	−10.5369	+	3.83513i	−0.375125	+	0.136534i
$790$	6.32040	−	3.64908i	0.224870	−	0.129829i
$791$	30.0657	−	5.02904i	1.06901	−	0.178812i
$792$	−7.62693	+	9.08942i	−0.271011	+	0.322978i
$793$	36.9910	−	6.52251i	1.31359	−	0.231621i
$794$	2.36915	−	13.4361i	0.0840781	−	0.476830i
$795$	−5.50184	−	31.2025i	−0.195130	−	1.10664i
$796$	−7.62157	−	9.08303i	−0.270139	−	0.321939i
$797$	12.7741			0.452481			0.226241	−	0.974071i	$-0.427356\pi$
$797$	12.7741			0.452481			0.226241	+	0.974071i	$0.427356\pi$
$798$	6.74310	−	0.219184i	0.238703	−	0.00775903i
$799$	−2.53947			−0.0898398
$800$	6.31763	+	7.52905i	0.223362	+	0.266192i
$801$	−0.293180	−	1.66271i	−0.0103590	−	0.0587489i
$802$	0.982854	−	5.57404i	0.0347058	−	0.196826i
$803$	62.2716	−	10.9802i	2.19752	−	0.387482i
$804$	−4.54405	+	5.41539i	−0.160256	+	0.190986i
$805$	8.30423	−	22.2058i	0.292686	−	0.782651i
$806$	1.61183	−	0.930591i	0.0567743	−	0.0327787i
$807$	−4.43296	+	1.61346i	−0.156047	+	0.0567966i
$808$	−4.83725	−	4.05893i	−0.170174	−	0.142793i
$809$	−26.8627			−0.944441			−0.472221	−	0.881480i	$-0.656547\pi$
$809$	−26.8627			−0.944441			−0.472221	+	0.881480i	$0.656547\pi$
$810$	1.52454			0.0535668
$811$	−5.39323	−	4.52546i	−0.189382	−	0.158910i	0.543167	−	0.839625i	$-0.317225\pi$
$811$	−5.39323	−	4.52546i	−0.189382	−	0.158910i	−0.732549	+	0.680714i	$0.761669\pi$
$812$	−7.50231	−	1.39103i	−0.263279	−	0.0488156i
$813$	4.72083	+	12.9704i	0.165567	+	0.454891i
$814$	−8.91077	−	3.24326i	−0.312322	−	0.113676i
$815$	−4.88940	+	13.4335i	−0.171268	+	0.470556i
$816$	5.14484	+	2.97038i	0.180106	+	0.103984i
$817$	44.0423	−	9.65583i	1.54084	−	0.337815i
$818$		−	21.2227i		−	0.742036i
$819$	1.60395	−	8.65066i	0.0560466	−	0.302279i
$820$	7.98605	+	9.51740i	0.278885	+	0.332362i
$821$	−12.5530	−	10.5332i	−0.438101	−	0.367611i	0.396897	−	0.917863i	$-0.370087\pi$
$821$	−12.5530	−	10.5332i	−0.438101	−	0.367611i	−0.834998	+	0.550253i	$0.814531\pi$
$822$	−3.65816	−	4.35962i	−0.127593	−	0.152059i
$823$	34.0850	−	12.4059i	1.18813	−	0.432444i	0.329063	−	0.944308i	$-0.393267\pi$
$823$	34.0850	−	12.4059i	1.18813	−	0.432444i	0.859067	+	0.511864i	$0.171045\pi$
$824$			36.9515i			1.28727i
$825$	4.96626	+	8.60181i	0.172903	+	0.299477i
$826$	−5.14845	+	2.91236i	−0.179137	+	0.101334i
$827$	19.5027	+	3.43884i	0.678174	+	0.119580i	0.502117	−	0.864800i	$-0.332555\pi$
$827$	19.5027	+	3.43884i	0.678174	+	0.119580i	0.176057	+	0.984380i	$0.443666\pi$
$828$	−2.85009	+	4.93651i	−0.0990476	+	0.171555i
$829$	−10.7647	−	18.6449i	−0.373872	−	0.647565i	0.616286	−	0.787523i	$-0.288637\pi$
$829$	−10.7647	−	18.6449i	−0.373872	−	0.647565i	−0.990157	+	0.139958i	$0.955303\pi$
$830$	6.28714	+	17.2738i	0.218230	+	0.599581i
$831$	3.56556	+	20.2213i	0.123688	+	0.701470i
$832$	−2.86701	+	1.04351i	−0.0993958	+	0.0361771i
$833$	−0.354590	+	20.1477i	−0.0122858	+	0.698075i
$834$	−1.85645	−	10.5284i	−0.0642835	−	0.364570i
$835$	16.3201	−	9.42240i	0.564780	−	0.326076i
$836$	−15.2468	−	37.0542i	−0.527323	−	1.28155i
$837$	−0.478361	+	0.828545i	−0.0165346	+	0.0286387i
$838$	−0.139135	+	0.116748i	−0.00480633	+	0.00403299i
$839$	34.9150	−	29.2972i	1.20540	−	1.01145i	0.205942	−	0.978564i	$-0.433974\pi$
$839$	34.9150	−	29.2972i	1.20540	−	1.01145i	0.999459	−	0.0328875i	$-0.0104703\pi$
$840$	7.48902	−	12.7117i	0.258396	−	0.438596i
$841$	−24.4072	−	8.88349i	−0.841628	−	0.306327i
$842$	−0.517266	+	2.93356i	−0.0178261	+	0.101097i
$843$	10.8076	−	6.23976i	0.372233	−	0.214909i
$844$			23.0152i			0.792218i
$845$	1.73084	+	4.75544i	0.0595426	+	0.163592i
$846$	0.0896153	−	0.508234i	0.00308104	−	0.0174734i
$847$	8.61942	+	51.5305i	0.296167	+	1.77061i
$848$	21.7291	+	12.5453i	0.746180	+	0.430807i
$849$	−4.96590	−	0.875622i	−0.170429	−	0.0300513i
$850$	−2.31082	+	1.93901i	−0.0792606	+	0.0665075i
$851$	−9.89876	−	1.74542i	−0.339325	−	0.0598322i
$852$	8.90904	−	24.4774i	0.305219	−	0.838582i
$853$	−28.2173	+	4.97547i	−0.966142	+	0.170357i	−0.634393	−	0.773011i	$-0.718750\pi$
$853$	−28.2173	+	4.97547i	−0.966142	+	0.170357i	−0.331749	+	0.943368i	$0.607639\pi$
$854$	−2.88429	−	17.2435i	−0.0986983	−	0.590059i
$855$	−5.26871	+	10.0635i	−0.180186	+	0.344165i
$856$	7.21966	+	12.5048i	0.246763	+	0.427406i
$857$	48.2861	+	17.5747i	1.64942	+	0.600340i	0.988649	−	0.150247i	$-0.0480068\pi$
$857$	48.2861	+	17.5747i	1.64942	+	0.600340i	0.660772	+	0.750587i	$0.270229\pi$
$858$	10.6233	−	1.87317i	0.362672	−	0.0639489i
$859$	13.9944	−	16.6779i	0.477484	−	0.569043i	−0.472504	−	0.881328i	$-0.656650\pi$
$859$	13.9944	−	16.6779i	0.477484	−	0.569043i	0.949989	+	0.312285i	$0.101094\pi$
$860$	15.2840	−	41.9924i	0.521179	−	1.43193i
$861$	3.86223	−	6.55568i	0.131624	−	0.223417i
$862$	2.61553	−	4.53024i	0.0890854	−	0.154301i
$863$	−18.0328	−	10.4112i	−0.613843	−	0.354402i	0.160625	−	0.987015i	$-0.448649\pi$
$863$	−18.0328	−	10.4112i	−0.613843	−	0.354402i	−0.774468	+	0.632613i	$0.781982\pi$
$864$	−3.52694	+	4.20324i	−0.119989	+	0.142997i
$865$	0.945830	−	1.12720i	0.0321592	−	0.0383258i
$866$	−13.9018	−	8.02621i	−0.472402	−	0.272742i
$867$	4.35659	−	7.54584i	0.147958	−	0.256270i
$868$	2.06605	+	3.65234i	0.0701263	+	0.123969i
$869$	−9.07884	+	24.9439i	−0.307979	+	0.846165i
$870$	−1.70478	+	2.03168i	−0.0577975	+	0.0688804i
$871$	13.9651	−	2.46243i	0.473190	−	0.0834361i
$872$	29.0821	+	10.5850i	0.984843	+	0.358453i
$873$	2.66044	+	4.60802i	0.0900423	+	0.155958i
$874$	4.69378	+	7.40597i	0.158770	+	0.250511i
$875$	14.0712	+	17.0723i	0.475695	+	0.577149i
$876$	18.6170	−	3.28268i	0.629010	−	0.110911i
$877$	0.912758	−	2.50778i	0.0308217	−	0.0846818i	−0.923327	−	0.384014i	$-0.874542\pi$
$877$	0.912758	−	2.50778i	0.0308217	−	0.0846818i	0.954149	+	0.299332i	$0.0967638\pi$
$878$	21.6366	+	3.81511i	0.730198	+	0.128754i
$879$	−14.4938	+	12.1618i	−0.488865	+	0.410206i
$880$	−29.3682	−	5.17841i	−0.990002	−	0.174564i
$881$	−37.3122	−	21.5422i	−1.25708	−	0.725775i	−0.284574	−	0.958654i	$-0.591852\pi$
$881$	−37.3122	−	21.5422i	−1.25708	−	0.725775i	−0.972506	+	0.232879i	$0.925185\pi$
$882$	−4.01972	−	0.781957i	−0.135351	−	0.0263299i
$883$	3.56901	−	20.2409i	0.120107	−	0.681160i	−0.863988	−	0.503513i	$-0.832041\pi$
$883$	3.56901	−	20.2409i	0.120107	−	0.681160i	0.984094	−	0.177647i	$-0.0568484\pi$
$884$	−5.42760	−	14.9122i	−0.182550	−	0.501552i
$885$		−	9.95920i		−	0.334775i
$886$	5.14109	−	2.96821i	0.172718	−	0.0997189i
$887$	0.841273	−	4.77109i	0.0282472	−	0.160198i	−0.967421	−	0.253172i	$-0.918526\pi$
$887$	0.841273	−	4.77109i	0.0282472	−	0.160198i	0.995669	+	0.0929740i	$0.0296374\pi$
$888$	−5.87797	−	2.13941i	−0.197252	−	0.0717938i
$889$	−39.9946	−	23.5625i	−1.34138	−	0.790262i
$890$	−1.97177	+	1.65451i	−0.0660940	+	0.0554594i
$891$	−4.24773	+	3.56427i	−0.142304	+	0.119408i
$892$	0.737494	−	1.27738i	0.0246931	−	0.0427697i
$893$	3.04516	+	2.34798i	0.101902	+	0.0785721i
$894$	−4.40682	+	2.54428i	−0.147386	+	0.0850935i
$895$	−7.19307	−	40.7939i	−0.240438	−	1.36359i
$896$	10.1638	+	28.7082i	0.339548	+	0.959073i
$897$	10.7447	−	3.91073i	0.358753	−	0.130576i
$898$	1.05792	+	5.99975i	0.0353031	+	0.200214i
$899$	−0.569247	−	1.56399i	−0.0189854	−	0.0521621i
$900$	1.48473	+	2.57163i	0.0494911	+	0.0857211i
$901$	−17.4995	+	30.3101i	−0.582994	+	1.00978i
$902$	9.18724	+	1.61996i	0.305902	+	0.0539387i
$903$	−27.3665	−	0.240801i	−0.910701	−	0.00801334i
$904$	12.3272	+	21.3513i	0.409996	+	0.710133i
$905$		−	31.1863i		−	1.03667i
$906$	−1.01533	+	0.369548i	−0.0337319	+	0.0122774i
$907$	−7.54463	−	8.99134i	−0.250515	−	0.298553i	0.626102	−	0.779742i	$-0.284650\pi$
$907$	−7.54463	−	8.99134i	−0.250515	−	0.298553i	−0.876617	+	0.481189i	$0.840205\pi$
$908$	21.8390	+	18.3251i	0.724751	+	0.608138i
$909$	−1.89685	−	2.26058i	−0.0629145	−	0.0749786i
$910$	−12.6440	+	4.47645i	−0.419145	+	0.148393i
$911$			27.0146i			0.895032i	0.894276	+	0.447516i	$0.147691\pi$
$911$			27.0146i			0.895032i	−0.894276	+	0.447516i	$0.852309\pi$
$912$	−3.42296	−	8.31878i	−0.113346	−	0.275462i
$913$	−57.9025	−	33.4300i	−1.91629	−	1.10637i
$914$	7.10693	−	19.5261i	0.235076	−	0.645867i
$915$	27.6608	+	10.0677i	0.914438	+	0.332828i
$916$	−0.209755	−	0.576296i	−0.00693049	−	0.0190414i
$917$	9.95808	−	11.6577i	0.328845	−	0.384971i
$918$	−1.29006	−	1.08249i	−0.0425784	−	0.0357275i
$919$	30.0747			0.992073			0.496036	−	0.868302i	$-0.334788\pi$
$919$	30.0747			0.992073			0.496036	+	0.868302i	$0.334788\pi$
$920$	19.1743			0.632159
$921$	10.7647	+	9.03262i	0.354708	+	0.297635i
$922$	−2.05483	+	0.747896i	−0.0676722	+	0.0246307i
$923$	−45.2509	+	26.1256i	−1.48945	+	0.859936i
$924$	4.01233	+	23.9874i	0.131996	+	0.789127i
$925$	−3.36578	+	4.01118i	−0.110666	+	0.131887i
$926$	−15.4058	+	2.71646i	−0.506267	+	0.0892685i
$927$	−2.99863	+	17.0061i	−0.0984880	+	0.558553i
$928$	−1.65754	−	9.40037i	−0.0544114	−	0.308582i
$929$	9.54938	+	11.3805i	0.313305	+	0.373382i	0.899600	−	0.436715i	$-0.143858\pi$
$929$	9.54938	+	11.3805i	0.313305	+	0.373382i	−0.586295	+	0.810098i	$0.699414\pi$
$930$	1.45856			0.0478280
$931$	19.0536	−	23.8319i	0.624458	−	0.781059i
$932$	−22.0143			−0.721102
$933$	0.177092	+	0.211050i	0.00579772	+	0.00690946i
$934$	−2.70445	−	15.3377i	−0.0884922	−	0.501864i
$935$	7.22341	−	40.9660i	0.236231	−	1.33973i
$936$	7.00762	−	1.23563i	0.229051	−	0.0403879i
$937$	9.29905	−	11.0822i	0.303787	−	0.362039i	−0.592456	−	0.805603i	$-0.701842\pi$
$937$	9.29905	−	11.0822i	0.303787	−	0.362039i	0.896243	+	0.443564i	$0.146286\pi$
$938$	−1.08890	−	6.50988i	−0.0355538	−	0.212555i
$939$	16.5636	−	9.56298i	0.540532	−	0.312076i
$940$	3.58123	−	1.30346i	0.116807	−	0.0425142i
$941$	16.0661	+	13.4811i	0.523741	+	0.439470i	0.865933	−	0.500159i	$-0.166725\pi$
$941$	16.0661	+	13.4811i	0.523741	+	0.439470i	−0.342193	+	0.939630i	$0.611170\pi$
$942$	−13.2946			−0.433161
$943$	9.88857			0.322016
$944$	6.04159	+	5.06950i	0.196637	+	0.164998i
$945$	4.47822	−	5.24255i	0.145676	−	0.170540i
$946$	−11.4764	−	31.5311i	−0.373130	−	1.02517i
$947$	32.9269	+	11.9844i	1.06998	+	0.389441i	0.816169	−	0.577813i	$-0.196094\pi$
$947$	32.9269	+	11.9844i	1.06998	+	0.389441i	0.253811	+	0.967254i	$0.418316\pi$
$948$	−2.71425	+	7.45734i	−0.0881547	+	0.242203i
$949$	−32.8402	−	18.9603i	−1.06604	−	0.615478i
$950$	4.56379	−	0.188557i	0.148069	−	0.00611759i
$951$			26.1674i			0.848535i
$952$	−15.3631	+	5.43911i	−0.497921	+	0.176283i
$953$	−9.80370	−	11.6836i	−0.317573	−	0.378469i	0.583517	−	0.812101i	$-0.301676\pi$
$953$	−9.80370	−	11.6836i	−0.317573	−	0.378469i	−0.901090	+	0.433632i	$0.857232\pi$
$954$	−5.44854	−	4.57187i	−0.176403	−	0.148020i
$955$	−36.4529	−	43.4428i	−1.17959	−	1.40578i
$956$	26.7552	−	9.73808i	0.865324	−	0.314952i
$957$		−	9.64643i		−	0.311825i
$958$	11.0539	+	19.1460i	0.357137	+	0.618579i
$959$	−25.7374	−	0.226465i	−0.831103	−	0.00731295i
$960$	−2.35467	−	0.415192i	−0.0759967	−	0.0134003i
$961$	15.0423	−	26.0541i	0.485237	−	0.840455i
$962$	2.84339	+	4.92489i	0.0916745	+	0.158785i
$963$	2.30791	+	6.34094i	0.0743715	+	0.204334i
$964$	−6.87754	−	39.0045i	−0.221511	−	1.25625i
$965$	19.2365	−	7.00150i	0.619243	−	0.225386i
$966$	−1.77617	−	5.01691i	−0.0571475	−	0.161416i
$967$	−2.58439	−	14.6568i	−0.0831085	−	0.471332i	−0.997749	−	0.0670630i	$-0.978637\pi$
$967$	−2.58439	−	14.6568i	−0.0831085	−	0.471332i	0.914640	−	0.404269i	$-0.132474\pi$
$968$	−36.5946	+	21.1279i	−1.17619	+	0.679076i
$969$	11.6039	−	4.77472i	0.372772	−	0.153386i
$970$	4.05594	−	7.02510i	0.130228	−	0.225562i
$971$	−40.0378	+	33.5957i	−1.28488	+	1.07814i	−0.292323	+	0.956320i	$0.594428\pi$
$971$	−40.0378	+	33.5957i	−1.28488	+	1.07814i	−0.992552	+	0.121819i	$0.961127\pi$
$972$	−1.26992	+	1.06559i	−0.0407327	+	0.0341788i
$973$	−41.6582	−	24.5426i	−1.33550	−	0.786799i
$974$	7.95105	+	2.89395i	0.254768	+	0.0927280i
$975$	1.03435	−	5.86607i	0.0331256	−	0.187865i
$976$	−20.1875	+	11.6553i	−0.646187	+	0.373076i
$977$			39.3375i			1.25852i	0.777196	+	0.629259i	$0.216642\pi$
$977$			39.3375i			1.25852i	−0.777196	+	0.629259i	$0.783358\pi$
$978$	1.09760	+	3.01563i	0.0350974	+	0.0964293i
$979$	1.62569	−	9.21976i	0.0519573	−	0.294665i
$980$	−9.84136	−	28.5948i	−0.314371	−	0.913427i
$981$	12.5254	+	7.23153i	0.399905	+	0.230885i
$982$	−14.2560	−	2.51372i	−0.454928	−	0.0802160i
$983$	−4.29386	+	3.60298i	−0.136953	+	0.114917i	−0.708691	−	0.705519i	$-0.750714\pi$
$983$	−4.29386	+	3.60298i	−0.136953	+	0.114917i	0.571738	+	0.820436i	$0.306269\pi$
$984$	6.06034	+	1.06860i	0.193197	+	0.0340658i
$985$	−17.2541	+	47.4051i	−0.549760	+	1.51045i
$986$	2.88517	−	0.508733i	0.0918826	−	0.0162014i
$987$	−1.48447	−	1.80107i	−0.0472511	−	0.0573286i
$988$	−7.27935	+	22.9001i	−0.231587	+	0.728549i
$989$	−17.7838	−	30.8024i	−0.565491	−	0.979459i
$990$	7.94378	+	2.89130i	0.252470	+	0.0918915i
$991$	−27.8166	+	4.90483i	−0.883625	+	0.155807i	−0.597005	−	0.802237i	$-0.703643\pi$
$991$	−27.8166	+	4.90483i	−0.883625	+	0.155807i	−0.286620	+	0.958044i	$0.592532\pi$
$992$	−3.37430	+	4.02133i	−0.107134	+	0.127677i
$993$	−5.67878	+	15.6023i	−0.180211	+	0.495125i
$994$	11.9744	+	21.1682i	0.379804	+	0.671414i
$995$	−9.31964	+	16.1421i	−0.295452	+	0.511738i
$996$	−17.3108	−	9.99438i	−0.548513	−	0.316684i
$997$	10.2163	−	12.1753i	0.323553	−	0.385595i	−0.579610	−	0.814894i	$-0.696795\pi$
$997$	10.2163	−	12.1753i	0.323553	−	0.385595i	0.903162	+	0.429299i	$0.141239\pi$
$998$	2.10495	−	2.50858i	0.0666310	−	0.0794078i
$999$	−2.53159	−	1.46161i	−0.0800960	−	0.0462434i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	399.2.ck.a.10.6	yes	78
7.5	odd	6		399.2.cd.a.124.6	✓	78
19.2	odd	18		399.2.cd.a.325.6	yes	78
133.40	even	18	inner	399.2.ck.a.40.6	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.cd.a.124.6	✓	78	7.5	odd	6
399.2.cd.a.325.6	yes	78	19.2	odd	18
399.2.ck.a.10.6	yes	78	1.1	even	1	trivial
399.2.ck.a.40.6	yes	78	133.40	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 399 = 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	399.ck (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.376037 - 0.448144i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.287868 - 1.63258i) q^{4} +(-2.56641 + 0.452528i) q^{5} +(-0.376037 + 0.448144i) q^{6} +(0.436486 + 2.60950i) q^{7} +(-1.85315 + 1.06991i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(1.16786 + 0.979954i) q^{10} -5.54502 q^{11} -1.65776 q^{12} +(2.54738 + 2.13751i) q^{13} +(1.00529 - 1.17688i) q^{14} +(0.891305 + 2.44884i) q^{15} +(-1.93925 - 0.705829i) q^{16} +(0.984567 - 2.70508i) q^{17} +(0.506633 + 0.292505i) q^{18} +(-3.68173 + 2.33342i) q^{19} +4.32014i q^{20} +(2.49406 - 0.882990i) q^{21} +(2.08513 + 2.48497i) q^{22} +(2.63403 + 2.21021i) q^{23} +(1.37545 + 1.63920i) q^{24} +(1.68322 - 0.612643i) q^{25} -1.94537i q^{26} +(0.500000 + 0.866025i) q^{27} +(4.38586 + 0.0385916i) q^{28} +(-1.71323 - 0.302088i) q^{29} +(0.762269 - 1.32029i) q^{30} +(0.478361 + 0.828545i) q^{31} +(1.87665 + 5.15604i) q^{32} +(0.962883 + 5.46078i) q^{33} +(-1.58250 + 0.575982i) q^{34} +(-2.30107 - 6.49952i) q^{35} +(0.287868 + 1.63258i) q^{36} +(-2.53159 + 1.46161i) q^{37} +(2.43018 + 0.772490i) q^{38} +(1.66269 - 2.87986i) q^{39} +(4.27177 - 3.58444i) q^{40} +(2.20303 - 1.84856i) q^{41} +(-1.33356 - 0.785660i) q^{42} +(-9.72015 - 3.53785i) q^{43} +(-1.59623 + 9.05268i) q^{44} +(2.25686 - 1.30300i) q^{45} -2.01155i q^{46} +(-0.301717 - 0.828962i) q^{47} +(-0.358359 + 2.03235i) q^{48} +(-6.61896 + 2.27802i) q^{49} +(-0.907506 - 0.523949i) q^{50} +(-2.83495 - 0.499878i) q^{51} +(4.22296 - 3.54348i) q^{52} +(-11.9733 - 2.11122i) q^{53} +(0.200085 - 0.549730i) q^{54} +(14.2308 - 2.50928i) q^{55} +(-3.60081 - 4.36878i) q^{56} +(2.93730 + 3.22060i) q^{57} +(0.508858 + 0.881367i) q^{58} +(-3.59116 - 1.30708i) q^{59} +(4.25450 - 0.750184i) q^{60} +(7.26059 - 8.65283i) q^{61} +(0.191426 - 0.525938i) q^{62} +(-1.30266 - 2.30284i) q^{63} +(-0.458748 + 0.794574i) q^{64} +(-7.50491 - 4.33296i) q^{65} +(2.08513 - 2.48497i) q^{66} +(2.74107 - 3.26668i) q^{67} +(-4.13282 - 2.38609i) q^{68} +(1.71924 - 2.97781i) q^{69} +(-2.04743 + 3.47527i) q^{70} +(-5.37413 + 14.7653i) q^{71} +(1.37545 - 1.63920i) q^{72} +(-11.2302 + 1.98018i) q^{73} +(1.60699 + 0.584895i) q^{74} +(-0.895624 - 1.55127i) q^{75} +(2.74964 + 6.68243i) q^{76} +(-2.42033 - 14.4697i) q^{77} +(-1.91582 + 0.337811i) q^{78} +(1.63730 - 4.49843i) q^{79} +(5.29632 + 0.933884i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-1.65684 - 0.292146i) q^{82} +(10.4422 + 6.02883i) q^{83} +(-0.723591 - 4.32593i) q^{84} +(-1.30268 + 7.38788i) q^{85} +(2.06968 + 5.68639i) q^{86} +1.73966i q^{87} +(10.2757 - 5.93270i) q^{88} +(-0.293180 + 1.66271i) q^{89} +(-1.43260 - 0.521422i) q^{90} +(-4.46592 + 7.58038i) q^{91} +(4.36660 - 3.66401i) q^{92} +(0.732891 - 0.614969i) q^{93} +(-0.258037 + 0.446933i) q^{94} +(8.39290 - 7.65461i) q^{95} +(4.75183 - 2.74347i) q^{96} +(-0.923961 - 5.24005i) q^{97} +(3.50985 + 2.10962i) q^{98} +(5.21062 - 1.89651i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q - 6 q^{7} + 12 q^{10} + 6 q^{11} + 72 q^{12} + 3 q^{13} - 15 q^{14} + 18 q^{19} + 9 q^{21} - 12 q^{22} + 30 q^{23} - 9 q^{24} + 18 q^{25} + 39 q^{27} - 9 q^{28} - 6 q^{29} - 18 q^{31} - 51 q^{32} - 12 q^{33}+ \cdots - 6 q^{99}+O(q^{100}) \) 78 * q - 6 * q^7 + 12 * q^10 + 6 * q^11 + 72 * q^12 + 3 * q^13 - 15 * q^14 + 18 * q^19 + 9 * q^21 - 12 * q^22 + 30 * q^23 - 9 * q^24 + 18 * q^25 + 39 * q^27 - 9 * q^28 - 6 * q^29 - 18 * q^31 - 51 * q^32 - 12 * q^33 + 30 * q^34 + 33 * q^35 + 18 * q^37 - 57 * q^38 - 18 * q^40 - 63 * q^41 - 27 * q^42 - 51 * q^43 - 36 * q^44 + 9 * q^45 - 84 * q^47 + 18 * q^49 - 27 * q^50 - 18 * q^51 + 18 * q^52 - 45 * q^53 + 30 * q^55 + 33 * q^56 - 6 * q^57 - 18 * q^58 - 24 * q^59 + 66 * q^61 + 171 * q^62 + 6 * q^63 + 18 * q^64 - 99 * q^65 - 12 * q^66 - 24 * q^67 - 12 * q^69 - 150 * q^70 - 66 * q^71 - 9 * q^72 + 3 * q^73 + 18 * q^74 - 36 * q^75 - 12 * q^76 + 21 * q^77 + 75 * q^78 + 45 * q^79 + 78 * q^80 - 24 * q^82 - 72 * q^83 - 9 * q^84 + 60 * q^85 - 9 * q^86 - 108 * q^88 + 48 * q^89 - 33 * q^90 - 54 * q^91 - 102 * q^92 + 9 * q^93 - 66 * q^94 - 84 * q^95 + 75 * q^97 - 39 * q^98 - 6 * q^99

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